GATE CSE 2007 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2007

MCQ (Single Correct Answer)

-0.6

Which one of these first-order logic formulae is valid?

$$\forall x\left( {P\left( x \right) \Rightarrow Q\left( x \right)} \right) \Rightarrow \left( {\left( {\forall xP\left( x \right)} \right) \Rightarrow \left( {\forall xQ\left( x \right)} \right)} \right)$$

$$\exists x\left( {P\left( x \right) \vee Q\left( x \right)} \right) \Rightarrow \left( {\left( {\exists xP\left( x \right)} \right) \Rightarrow \left( {\exists xQ\left( x \right)} \right)} \right)$$

$$\exists x\left( {P\left( x \right) \wedge Q\left( x \right)} \right) \Leftrightarrow \left( {\left( {\exists xP\left( x \right)} \right) \wedge \left( {\exists xQ\left( x \right)} \right)} \right)$$

$$\forall x\exists yP\left( {x,y} \right) \Rightarrow \exists y\forall xP\left( {x,y} \right)$$

GATE CSE 2007

MCQ (Single Correct Answer)

-0.3

Let $$S$$ be a set6 of $$n$$ elements. The number of ordered pairs in the largest and the smallest equivalence relations on $$S$$ are

$$n$$ and $$n$$

$${n^2}\,$$ and $$n$$

$${n^2}\,$$ and $$0$$

$$n$$ and $$1$$

GATE CSE 2007

MCQ (Single Correct Answer)

-0.6

Consider the following Hasse diagrams.
GATE CSE 2007 Discrete Mathematics - Set Theory & Algebra Question 44 English 1

GATE CSE 2007 Discrete Mathematics - Set Theory & Algebra Question 44 English 2

GATE CSE 2007 Discrete Mathematics - Set Theory & Algebra Question 44 English 3

GATE CSE 2007 Discrete Mathematics - Set Theory & Algebra Question 44 English 4

Which all of the above represent a lattice?

(i) and (iv) only

(ii) and (iii) only

(iii) only

(i), (ii) and (iv) only

GATE CSE 2007

MCQ (Single Correct Answer)

-0.3

Suppose there are two coins. The first coin gives heads with probability 5/8 when tossed, while the second coin gives heads with probability 1/4. On e of the two coins is picked up at random with equal probability and tossed. What is the probability of obtaining heads?

7/8

$${\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}$$

7/16

5/32

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