| 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: \[A\,\,*\,\,B,\text{ }C\,\$\,D,\text{}A\,\Delta\,C,\text{}D\,\,\#\,\,E\] |
| Conclusions I. \[C\,\,*\,\,B\] II. \[C\,\#\,E\] |
| 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: \[A\,\,*\,\,B\text{ }\to \text{ }A\,\,=\,\,B\] \[C\,\$\,D\,\,\,\to\,\,C<D\] \[A\,\Delta \,C\,\,\to \,\,A>C\] \[D\,\,\#\,\,E\,\,\to \,\,D\le E\] \[\therefore \text{ }E\,\,\ge \,\,D>C<A=B\] Conclusions I. \[C\,\,*\,\,B\text{ }\to \text{ }C\,\,=\,\,B\] (5) II.\[C\,\,\#\,\,E\,\,\to \,\,C\le E\] (5)
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