Exams › GATE › Technical

Consider the following logical inferences. I1: If it rains, then the cricket match will not be played. The cricket match was played. Inference: There was no rain. I2: If it rains, then the cricket match will not be played. It did not rain. Inference: The cricket match was played. Which of the following is true?

1. Both I1 and I2 are correct inferences
2. I1 is correct but I2 is not a correct inference
3. I1 is not correct but I2 is a correct inference
4. Both I1 and I2 are not correct inferences

Correct answer: I1 is correct but I2 is not a correct inference

Solution

In I1, if rain implies no match, then the match being played means rain did not occur, so the inference is valid. In I2, not raining does not necessarily imply that the match was played, so that inference is invalid.

Related GATE Technical questions

• Given that A and B are not null sets, which of the following statements regarding probability is/are CORRECT?
• Consider the following two statements about the function \(f(x)=|x|\): P. \(f(x)\) is continuous for all real values of \(x\). Q. \(f(x)\) is differentiable for all real values of \(x\). Which of the following is true?
• A company assembles computers. The probability of a faulty assembly of any computer is p. The company therefore subjects each computer to a testing process. This testing process gives the correct result for any computer with probability q. What is the probability of a computer being declared faulty?
• What is the probability that a divisor of $10^9$ is a multiple of $10^5$?
• Consider the following matrix: \[ A = \begin{bmatrix} 2 & 3 \\ x & y \end{bmatrix} \] If the eigenvalues of $A$ are 4 and 8, then
• Consider a random variable $X$ that takes values $+1$ and $-1$ with probability $0.5$ each. The values of the cumulative distribution function $F(x)$ at $x=-1$ and $x=+1$ are

⚔️ Practice GATE Technical free + battle 1v1 →