Exams › JEE Main › Maths

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

1. (1) (A) is false, but (B) and (C) are true
2. (2) (A) and (C) are true while (B) is false
3. (3) (A) is true while (B) and (C) are false
4. (4) (A) and (B) are false while (C) is true

Correct answer: (1) (A) is false, but (B) and (C) are true

Solution

Statement (A) is false because 3 + 3 equals 6, not 7, making the implication false. Statement (B) is also false since the earth is not flat, but in logic, a false premise can lead to a true conclusion, which makes (C) true. Therefore, (A) is false while (B) and (C) are true.

Related JEE Main Maths questions

• Let $T(k)$ denote the claim that $1+3+5+\cdots+(2k-1)=k^2+10$. Which statement below is correct?
• Let $S(k)$ denote the sum $1+3+5+\cdots+(2k-1)$, and suppose it is given by $k^2+3$. Which statement below is true?
• For every natural number $n$, which of the following inequalities is true?
• Let \(p\), \(q\), and \(r\) be arbitrary logical propositions. Which of the following equivalences is correct?
• The proposition \(~(p\to q)\to[(\sim p)\lor(\sim q)]\) is best classified as
• For integers $m$ and $n$, each exceeding 1, let the statements be: $P$: $m$ is a divisor of $n$; $Q$: $m$ is a divisor of $n^2$; and $R$: $m$ is a prime number. Which of the following implications is true?

⚔️ Practice JEE Main Maths free + battle 1v1 →