Question

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

P @ Q → P≥ Q

P# Q→P≤Q

P$ Q→ P<Q

P®Q → P> Q

P % Q → P = Q

Statements:

M®N

N # O

Conclusions:

1. M®O

2.M@ O

• A. If only conclusion I is true.
• B. If only conclusion Il is true.
• C. If only conclusion Ill is true.
• D. Neither I nor Il is true

Answer 1

Answer:

D. Neither I nor Il is true

Let's translate the statements:

• M ® N ⇒ M > N

• N # O ⇒ N ≤ O

So we have:

M > N and N ≤ O

Now check the conclusions:

Conclusion 1: M ® O

⇒ M > O

This does not necessarily follow.

Example:

• M = 5, N = 3, O = 6

Then:

• M > N ✓

• N ≤ O ✓

• M > O? ⇒ 5 > 6 ✗

So Conclusion 1 does not follow.

Conclusion 2: M @ O

⇒ M ≥ O

This also does not necessarily follow.

Using the same example:

• M = 5, O = 6

• M ≥ O? ⇒ 5 ≥ 6 ✗

So Conclusion 2 does not follow.

Can both conclusions be false?

Yes, as shown in the example above.

Answer: Neither Conclusion 1 nor Conclusion 2 follows.