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