| Direction: In each question given below certain symbols are used with the following meaning. |
| \[P\,\Delta \,Q\] means ?P is greater than Q?. |
| \[P\,\,\,\,Q\] means ?P is either greater than or equal to Q?. |
| \[P\,\,*\,\,Q\] means ?P is equal to Q.?. |
| \[\,\,\#\,\,Q\] means ?P is either smaller than or equal to Q?. |
| \[P\,\,\$\,\,Q\] means ?P is smaller than Q?. |
| Statements: \[A*B,\,\,C\,\,\#\,\,D,\,\,A\,\Delta \,F,\,\,B\,\,C\] |
| Conclusions I. \[B\,\Delta \,F\] |
| II. \[A\,\,\,\,C\] |
| 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. |
A) if only Conclusion I is true.
B) if only Conclusion II is true.
C) if either Conclusion I or II is true.
D) if neither Conclusion I nor II is true.
E) if both Conclusions I & II are true.
Correct Answer: E
Solution :
\[P\,\Delta \,Q\,\,\to \,\,P>Q\] \[P\,\,\,\,Q\,\,\,\,\to \,\,\,P\,\,\ge \,\,Q\] \[P\,\,*\,\,Q\,\,\,\to \,\,P\,\,=\,\,Q\] \[P\,\text{ }\!\!\#\!\!\text{ }\,Q\,\,\to \,\,P\,\,\le \,\,Q\] \[P\,\$\,Q\,\,\toP\,\,<\,\,Q\] (e) Statements: \[A\,\,*\,\,B\,\,\to \,\,A\,\,=\,\,B\] \[C\,\,\#\,\,D\,\,\to \,\,C\,\,\le \,\,D\] \[A\,\Delta \,F\,\,\to \,\,A\,\,>\,\,F\] \[B\,\,\,\,C\,\,\to \,\,B\,\,\ge \,\,C\] \[\therefore \,\,\,\text{ }D\,\,\ge \,\,C\,\,\le \,\,B=A>F\] Conclusions I. \[B\,\Delta \,F\,\,\to \text{ }B\text{ }>F\] (3) II. \[A\,\,\,\,C\,\,\,\to \,\,\,A\,\,\ge \,\,C\] (3)
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