# 12th Class Mental Ability Coding-Decoding Notes - Statements and Conclusion Symbols

Notes - Statements and Conclusion Symbols

Category : 12th Class

Statements and Conclusions in Symbols

Introduction:

In this type of question there is a combination of two types of problem (i) coding (ii) critical reasoning. You have to         solve these questions keeping in mind that you have to first solve the coding riddle before you begin solving the critical reasoning aspect of it. Given below are a full illustrations which will help you understand this type of question.

Example:

Directions (1 - 5): In the following questions, the symbols @, , *, $and # are used with the following meaning: $A\,\,\#\,\,B$ means A is not greater than B. $A\,\\,B$ means is neither smaller nor equal to B. $A\,?\,B$ means A is neither smaller nor greater than B. $A\,*\,B$ means A is neither greater nor equal to B. $A\,\,\,\,B$ means A is not smaller than B. Now in each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below then is/are definitely true? Give answer (a) if only conclusion I is true. Give answer (b) if only conclusion II is true. Give answer (c) if either conclusion I or II is true. Give answer (d) if neither conclusion I nor II is true. Give answer (e) if both conclusions I and II are true. 1. Statements: $M\N,$ $G\text{ }\text{ }H,$ $N\text{ }?\text{ }H$ Conclusions I. $M\text{ }\text{ }H$ 1. $H\text{ }\\text{}G$ 1. Statements: $G\text{ }\text{ }M,$ $N\text{ }\#\text{ }L,$ $G\text{ }*\text{ }L$ Conclusions I. $G\text{ }\text{ }N$ 1. $L\text{ }\\text{}M$ 1. Statements: $P\text{ }\\text{}Q,$ $R\text{ }\text{ }\,$ $P\text{ }*\text{ }R$ Conclusions I. $Q\text{ }*\text{ }R$ 1. $P\text{ }\#\text{ }S$ 1. Statements: $U\text{ }\\text{}V,$ $W\text{ }*\text{ }X,$ $U\text{ }\text{ }X$ Conclusions I. $VX$ 1. $V\text{ }*\text{ }X$ 1. Statements: $K\text{ }\#\text{ }T,$ $D\text{ }\\text{}F,$ $T\text{ }*\text{ }F$ Conclusions I. $K\text{ }*\text{ }D$ 1. $D\text{ }\\text{}T$ Now, meaning of the symbols are: $\mathbf{\#}\to \,\,\le$ (either less than or equal to); $\\,\,\to\,\,>$ (greater than); $\mathbf{?}\to \,\,=$ (equal to); $\mathbf{*}\,\,\to \,\,<$ (less than); $\mathbf{}\,\,\to \,\,\ge$ (either greater than or equal to). 1. $M\,\,>\,\,N,\text{ }G\text{ }\ge \text{ }H,\text{ }N\,\,=\,\,H,$ $\therefore \,\,\,M\text{ }>\text{ }H$, Hence I is not definitely true. There is no direct relation between M and F and hence II is not true. 1. $G\,\,\ge \,\,M,\text{ }N\,\,\le \,\,L,\text{ }G\,\,<\,\,L;\,\,\,\,\therefore$, G and N are not directly related, hence I is not true. 2. $P>Q,\text{ }R\,\,\ge \,\,S,\text{ }P\,\,<\,\,R,$ Therefore from (i) and (iii) $R>P>Q$ or $Q<R$, Hence I is true P and S are not directly related and so, II is not true. 1. $U>V,\,\,W<X,\,\,U\,\,\ge \,\,X$ $\therefore$ From (i) and (iii) $V\,\,<\,\,U\,\,\ge \,\,X$. It means either $U\text{ }>\text{ }X$, or $V\text{ }=\text{ }K$, or $U\text{ }<\text{ }X$. Hence either I or II is true. 1. $K\,\,\ge \,\,T,\,\,D\,\,>\,\,F,\,\,T\,\,<\,\,F$. After combining the three. We get $D\,\,>\,\,F\,\,>\,\,T\,\,\ge \,\,K$. $\therefore \,\,\,\text{ }K\text{ }<\text{ }D$, Hence I is true. $D\text{ }>\text{ }T$, Hence II is true. Snap Test Directions (1 - 5): 8n the following questions, the symbols @, # ©,$ and H are used with the following meaning as illustrated below:

$\mathbf{P}\text{ }\\text{}\mathbf{Q}$ means ‘P is not smaller than Q’.

$\mathbf{P}\text{ }\text{ }\mathbf{Q}$ means ‘P is neither greater than nor equal to Q’.

$\mathbf{P}\,\,*\,\,\mathbf{Q}$ means ‘P is neither smaller than nor equal to Q’.

$\mathbf{P}\,\,\,\,\mathbf{Q}$ means ‘P is not greater than Q’.

$\mathbf{P}\text{ }\#\text{ }\mathbf{Q}$ means ‘P is neither greater than nor smaller than Q’.

Now in each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below then is / are definitely true?

Mark answer (a), if only conclusion I is true.

Mark answer (b), if only conclusion II is true,

Mark answer (c), if either conclusion I or II is true.

Mark answer (d), if neither conclusion I nor II is true and

Mark answer (e), if both conclusions I and II are true.

1. Statements: $R\,\,*\,\,N,\,\,N\,\,\\,\,W,\,\,W\,\,\#\,\,V$

Conclusions I. $V\text{ }\text{ }R$

1.            $R\text{ }*\text{ }W$

1. Statements: $H\,\,\#\,\,D,\,\,A\,\,*\,\,D,\,\,A\,\,\,\,M$

Conclusions     I. $M\,\,\#\,\,H$

1.         $M\,\,\,\,D$

1. Statements: $M\,\,\,\,R,\,\,R\,\,\,\,D,\,\,D\,\,\#\,\,N$

Conclusions I.  $N\,\,\#\,\,R$

1.            $N\,\,*\,\,R$

1. Statements: $J\text{ }\text{ }N,\text{ }K\text{ }\text{ }N,\text{ }T\text{ }\\text{}K$

Conclusions I. $T\,\,*\,\,J$

1. $J\,\,\,\,K$

1. Statements: $K\,\,\#\,\,T,\,\,T\,\,*\,\,F,\,\,F\,\,\,\,B$

Conclusions I. $F\,\,\,\,K$

1.             $B\,\,\text{ }K$

Explanation (1 to 5)

$\begin{array}{*{35}{l}} \=P\geQ\\=P<Q\\*=P>Q\\=p\leQ\\\#=P=Q\\\end{array}$

1.          (e)

Statements:     $R>N,\,\,N\,\,\ge \,\,W,\,\,W\,\,=\,\,V$

$\therefore \,$        $\therefore \,\,\,R>N\ge W=V$

Conclusions I. $V\text{ }<\text{ }R\text{ }....$ (3)

1.             $R\,\,>\,\,W$ .... (3)

1. (d)

Statements:     $H=D,\,\,A>D,\,\,A\,\,\le \,\,M$

$\therefore \,\,\text{ }M\,\,\ge \,\,A\,\,>\,\,D\,\,=\,\,H$

Conclusions: I. $M\text{ }=\text{ }H$.... (5)

1.            $M<D$.... (5)

1.          (c)

Statements:     $M\,\,<\,\,R,\,\,R\,\,\le \,\,D,\,\,D\,\,=\,\,N$

$\therefore$            $M\,\,>\,\,R\,\,\le \,\,D\,\,=\,\,N$

Conclusions I.  $N\,\,=\,\,R$ .... (3)

1.             $N>R$ .... (3)

1.         (d)

Statements:     $J\,\,\le \,\,N,\text{ }K\,\,<\,\,N,\text{ }T\,\,\ge \,\,K$

$\therefore$          $J\,\,\le \,\,N\,\,>\,\,K\,\,\le \,\,T$

Conclusions I.  $T\text{ }>\text{ }J$ .... (3)

1.                      $J\,\,<\,\,K$.... (5)
2. (a)

Statements:     $K\,\,=\,\,\,T,\text{ }T\,\,>\,\,F,\text{ }F\,\,<\,\,B$

$\therefore$          $K=T>F<B$

Conclusions I.  $F\,\,<\,\,K$ .... (3)

$B\,\,<\,\,K$.... (5)

Direction $\left( \mathbf{6-11} \right)\mathbf{:}$ In the following the symbols @, ©, \$, # and A are used with the following meaning as illustrated below:

$XY$ means ‘X is not greater than Y’.

$X\text{ }\#\text{ }Y$ means ‘X is neither smaller than nor equal to Y’.

$X\text{ }\text{ }Y$ means ‘X is not smaller than Y.

$X\text{ }\Delta \text{ }Y$ means ‘X is neither greater than nor smaller than Y’.

$X\text{ }\\text{}Y$ means ‘X is neither greater than nor equal to Y’.

Now in each of the following questions assuming the given statements to be true, find which of the two conclusions I & II given below them is/are definitely true?

Give answer (a) if only conclusion I is true.

Give answer (b) if only conclusion II is true.

Give answer (c) if either conclusion I or SS is true.

Give answer (d) if neither conclusion I nor II is true.

Give answer (e) if both conclusion I and II are true.

1. Statements: $G\,\,\\,\,T,\,\,N\,\,\Delta\,T,\,\,O\,\,N$

Conclusions I.  $T\,\Delta \,O$

1. $0\,\,\#\,\,G$
2. Statements: $P\,\Delta \text{ }J,\,\,J\,\,\#\,\,L,\text{ }R\text{ }\text{ }L$

Conclusions     I. $P\,\,\#\,\,L$

1.   $R\,\Delta \,P$

1. Statements: $M\,\Delta \,A,\,\,A\,\,\,Q,\,\,B\,\,\#\,Q$

Conclusions I. $M\,\\,Q$

1. $Q\,\Delta \,M$

1. Statements: $D\,\,\,\,R,\,\,S\,\\,R,\,\,H\,\Delta\,S$

Conclusions I. $D\,\,\#\,S$

1. $H\,\Delta \,R$

1. Statements: $P\,\\,V,\,\,W\,\#\,V,\,\,U\,\Delta\,W$

Conclusions I. $U\,\,\#\,\,P$

1. $V\,\Delta \,U$

1. Statements: $I\text{ }\text{ }R,\text{ }C\text{ }\Delta \text{ I},\text{ }C\text{ }\text{ }E$

Conclusions I. $C\text{ }\text{ }R$

1.            $R\,\,\,\,E$

Explanation (6 to 11)

$\begin{array}{*{35}{l}} \,\,=\,\,X\,\,\le \,\,Y \\ \#\,\,=\,\,X\,\,>\,\,Y \\ \,\,=\,\text{ }X\,\,\ge \,\,Y \\ \Delta \,\,=\,\,X\,\,=\,\,Y \\ \\,\,=\,\,X\,\,<\,\,Y\\\end{array}$

1.       (b)

Statements:     $G\,\,<\,\,T,\,\,\,N=T,\,\,O\,\,\ge \,\,N$

$\therefore$           $O\text{ }\ge \text{ }N\text{ }=\text{ }T\text{ }>\text{ }G$

Conclusions I.  $T\,\,=\,\,O$ (5)

1.             $O\,\,>\,\,G\,\,\,$ (3)

1.        (a)

Statements:     $P\,\,\ge \,\,J,\,\,J\,\,>\,\,L,\text{ }R\,\,\le \,\,L$

$\therefore$          $~P\,\,\ge \,\,J\,\,>\,\,L\,\,\ge \,\,R$

Conclusions I.  $P\,\,>\,\,L$ (3)

$R\,\,=\,\,P$ (5)

1.          (c)

Statements:     $M=A,\text{ }A\le Q,\text{ }B>Q$

$\therefore$           $B>Q\text{ }\ge A=M$

Conclusions I.  $M\,\,<\,\,Q$ (3 5)

1.             $Q\,\,=\,\,M$ (5 3)

1.         (d)

Statements:     $D\,\,\le \,\,R,\,\,\,S\,\,<\,\,R,\text{ }H\,\,=\,\,S$

$\therefore$           $H\,\,=\,\,S\,\,<\,\,R\,\,\ge \,\,D$

Conclusions I.  $D\,\,>\,\,S$ (5)

1.            $H\,\,=\,\,R$ (5)

1.         (a)

Statements:     $P<V,\,\,W>V,\,\,U=W$

$\therefore$           $U=W>V>P$

Conclusions I.  $U\,\,>\,\,P$ (3)

1.            $V\,\,=\,\,U$ (5)

1.        (a)

Statements:     $1\,\,\,\ge \,\,R,\,\,C\,\,=\,\,1,\,\,C\,\,\ge \,\,E$

$\therefore$ $~~~~E\,\,\le \,\,C\,\,=\,\,I\,\,\ge \,\,R$

Conclusions I. $C\,\,>\,\,R$ (3)

1. $R\,\,<\,\,E$ (5)

Direction: Q. No. 12: In the given question, the symbols +, -, $\mathbf{\div }$ and $\mathbf{\times }$ are used with the following meaning.

$P\,\,+\,\,Q$ means ‘P is mother of Q’.

$PQ$ means ‘P is brother of Q’.

$P\,\,\div \,\,Q$ means ‘P is sister of Q’.

$P\times Q$ means ‘P is father of Q’.

1. Which of the following means T is niece of D?

(a) $D\,\,\div \,\,M\,\,+\,\,T$

(b) $D\,\,\div \,\,M\,\,+\,\,T\,\,\div \,\,R$

(c) $D\,\,-\,\,M\,\,\times \,\,T\,\,\div \,\,R$

(a) Only (b)                    (b) Only (c)

(c) Both (a) and (b)         (d) Both (b) and (c)

(e) None of these

Explanation: 12

1. (d)

From II

Statement:       $D\,\,\div \,\,M\,\,=\,\,D$ is sister of M.

$M\,\,\times \,\,T\,\,=\,\,M$ is mother of T

$T\,\,\div \,\,R\,\,=\,\,T$ is sister of R.

Hence T is nieces of D.

From III,

Statement:       $D\,\,-\,\,M\,\,=\,\,D$ is brother of M.

$M\,\,\times \,\,T\,\,=\,\,M$ is father of T.

$T\,\,\div \,\,R\,\,=\,\,T$ is sister of R.

$\therefore$             T is niece of D.

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##### Notes - Statements and Conclusion Symbols

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