| 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.?. |
| \[P\,\,\#\,\,Q\] means ?P is either smaller than or equal to Q?. |
| \[P\,\,\$\,\,Q\] means ?P is smaller than Q?. |
| Statements: \[A\,\,\,\,B,\text{ }B\,\,*\,\,C,\text{ }D\,\,\Delta \,\,A,\text{ }E\,\,\#\,\,D\] |
| Conclusions I. \[B\,*\,\,E\] |
| II.\[C\,\$\,A\] |
| 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: D
Solution :
\[P\,\Delta \,Q\,\,\to \,\,P>Q\] \[P\,\,\,\,Q\,\,\,\,\to \,\,\,P\,\,\ge \,\,Q\] \[P\,\,*\,\,Q\,\,\,\to \,\,P\,\,=\,\,Q\] \[P\,\text{ }\!\!\#\!\!\text{ }\,Q\,\,\to \,\,P\,\,\le \,\,Q\] \[P\,\$\,Q\,\,\toP\,\,<\,\,Q\] (d) Statements: \[A\,\,\,\,B\,\,\,\to \,\,\,A\,\,\ge \,\,B\] \[\,B*C\,\,\,\to \,\,\,B=C\] \[D\,\Delta \,A\,\,\,\,\to \,\,D>A\] \[E\,\,\#\,\,D\,\,\,\to \,\,E\le D\] \[\therefore \,\,\,\text{ }E\le D>A\ge \text{ }B=C\] Conclusions I. \[B\,\,*\,\,E\text{ }\to \text{ }B\,\,=\,\,E\] (5) II.\[C\,\$\,A\,\,\,\to\,C<A\] (5)
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