1
GATE CSE 2012
+1
-0.3
Consider the following logical inferences.
$${{\rm I}_1}:$$ If it rains then the cricket match will not be played. The cricket match was played.
Inference: there was no rain.

$${{\rm I}_2}:$$ 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?

A
Both $${{\rm I}_1}$$ and $${{\rm I}_2}$$ are correct inferences
B
$${{\rm I}_1}$$ is correct but $${{\rm I}_2}:$$ is not a correct inference
C
$${{\rm I}_1}$$ is not correct but $${{\rm I}_2}$$ is a correct inference
D
Both $${{\rm I}_1}$$ and $${{\rm I}_2}$$ are not correct inferences
2
GATE CSE 2012
+1
-0.3
What is the correct translation of the following statement into mathematical logic? "Some real numbers are rational"
A
$$\exists x\left( {real\left( x \right) \vee rational\left( x \right)} \right)$$
B
$$\forall x\left( {real\left( x \right) \to rational\left( x \right)} \right)$$
C
$$\exists x\left( {real\left( x \right) \wedge rational\left( x \right)} \right)$$
D
$$\exists x\left( {rational\left( x \right) \to real\left( x \right)} \right)$$
3
GATE CSE 2012
+1
-0.3
The truth table

Represents the Boolean function

A
$$X$$
B
$$X+Y$$
C
$$X \oplus Y$$
D
$$Y$$
4
GATE CSE 2012
+1
-0.3
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 + 1 are
A
0 and 0.5
B
0 and 1
C
0.5 and 1
D
0.25 and 0.75
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