Question

In the following questions the symbols $, @, ⊂, ⊃ and ≠ are used with the following meaning.

A $ B means A is greater than B

A @ B means A is either greater than or equal to B

A ⊂ B means is A is equal to B

A ⊃ B means A is smaller than B

A ≠ B means A is either smaller than or equal to B

Now assuming the given statements to be true, find which of the two conclusions I and II given below them is /are definitely true?

Statements :

P @ Q

M ≠ N

N ⊂ Q

Conclusions:

I. P $ M

II. N ≠ P

• A. If only conclusions I is true
• B. If only conclusions II is true
• C. If neither I nor II is true
• D. If both I and II are true,

Answer 1

The correct option is B If only conclusions II is true

P @ Q $\Rightarrow$ P $\ge$ Q
M $\ne$ N$\Rightarrow$ M $\le$ N
N $\subset$ Q $\Rightarrow$ N = Q
$\therefore$ M $\le$ N = Q $\le$ P
Conclusion
I. P $M$\Rightarrow$P>M-NotTrueII.N$\neq$P$\Rightarrow$N$\leq$ P -True
Hence only conclusion II is true.