MHT CET · Maths · Mathematical Reasoning

Consider the statements given by following :
(A) If \(3+3=7\), then \(4+3=8\).
(B) If \(5+3=8\), then earth is flat.
(C) If both \((\mathrm{A})\) and \((\mathrm{B})\) are true, then \(5+6=17\).
Then which of the following statements is correct?

A (A) is true while (B) and (C) are false.
B (A) and (C) are true while (B) is false.
C (A) and (B) are false, while (C) is true.
D (A) is false but (B) and (C) are true.

Verified Solution

Answer & Solution

Correct Answer

(B) (A) and (C) are true while (B) is false.

Step-by-step Solution

Detailed explanation

(A). Let \(\mathrm{p}: 3+3=7\)
\(q: 4+3=8\)
Truth value of p and q are F and F .
\(\therefore \quad \mathrm{p} \rightarrow \mathrm{q} \equiv \mathrm{T}\)
(B) Let \(\mathrm{p}: 5+3=8\),
q ; earth is flat
Truth value of p and q are T and F .
\(\therefore \quad \mathrm{p} \rightarrow \mathrm{q} \equiv \mathrm{F}\).
(C) Let p : Both (A) and (B) are true
\(q: 5+6=17\)
Truth values of \(p, q\) are false and false.
\(\therefore \quad \mathrm{p} \rightarrow \mathrm{q} \equiv \mathrm{~T}\)
\(\therefore \quad(\mathrm{A})\) and \((\mathrm{C})\) are true, while \((B)\) is false.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Consider the statements given by following :(A) If \(3+3=7\), then \(4+3=8\).(B) If \(5+3=8\), then earth is flat.(C) If both \((\mathrm{A})\) and \((\mathrm{B})\) are true, then \(5+6=17\).Then which of the following statements is correct?

Step-by-step Solution

Consider the statements given by following :
(A) If \(3+3=7\), then \(4+3=8\).
(B) If \(5+3=8\), then earth is flat.
(C) If both \((\mathrm{A})\) and \((\mathrm{B})\) are true, then \(5+6=17\).
Then which of the following statements is correct?