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Question

In the following questions, the symbols δ,%,$,# and @ are used with the following meaning as illustrated below.

′P $ Q′ means 'P is not smaller than Q'.

′P@Q′ means 'P is not greater than Q'.

′P δ Q′ means 'P is neither smaller than nor equal to Q'.

′P # Q′ means 'P is neither greater than nor equal to Q'.

′P % Q′ means 'P is neither smaller than nor greater than Q'.

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

Statements

F@N

NδR

H@R

Conclusions

I. HδN

II. F#R

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Solution

The correct option is **D** Neither conclusion I nor II is true

P $ Q ⇒ P ≥ Q

P @ Q ⇒ P ≤ Q

P δ Q ⇒ P > Q

P % Q⇒ P = Q

Statements: F @ N ⇒ F ≤ N,

F δ R ⇒ N > R

H @ R ⇒ H ≤ R

So, F ≤ N > R ≥ H

Conclusions

I. HδN ⇒ H > N (False)

II. F#R⇒F<R (False)

P $ Q ⇒ P ≥ Q

P @ Q ⇒ P ≤ Q

P δ Q ⇒ P > Q

P % Q⇒ P = Q

Statements: F @ N ⇒ F ≤ N,

F δ R ⇒ N > R

H @ R ⇒ H ≤ R

So, F ≤ N > R ≥ H

Conclusions

I. HδN ⇒ H > N (False)

II. F#R⇒F<R (False)

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