1
GATE CSE 2012
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+1
-0.3
The truth table GATE CSE 2012 Discrete Mathematics - Mathematical Logic Question 35 English

Represents the Boolean function

A
$$X$$
B
$$X+Y$$
C
$$X \oplus Y$$
D
$$Y$$
4
GATE CSE 2008
MCQ (Single Correct Answer)
+1
-0.3
A set of Boolean connectives is functionally complete if all Boolean function can be synthesized using those, Which of the following sets of connectives is NOT functionally complete?
A
EX-NOR
B
implication, negation
C
OR, negation
D
NAND
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