1. how many different equivalence relation with exactly three different equivalence classes are there on a set with five elements?

(1) 10

(2) 15

(3) 25

(4) 30

(1) 14,14

(2) 16,14

(3) 16,4

(4) 14,4

3. Suppose that R1 and R2 are reflexive relations on a set A.

Which of the following statement is correct?

(1) R1 ∩ R2 is reflexive and R1 ∩ R2 is irreflexive

(2) is irreflexive and R1 ∩ R2 is reflexive

(3) Both R1 ∩ R2 and R1 ∩ R2 are reflexive

(4) Both R1 ∩ R2 and R1 ∩ R2 are irreflexive

What is the probability that the opposite side is the same color as the one side we observe?

(1)3/4

(2) 2/3

(3) ½

(4) 1/3

(1) 2

(2) 4

(3) 5

(4) 6

(1) 1 Θ 0=1

(2) 1 Θ 1 Θ 1=1

(3) 1 Θ 1 Θ 0=1

(4) 1 Θ 1=0

(1) 16

(2) 32

(3) 48

(4) 64

(1) F=xy’+y’z

(2) F=xy’+x’y

(3) F=x’y+xz’

(4) F=x’z+xz’+xyz

(1) AB’

(2) AB’C

(3) A’B

(4) ABC

(1) No change

(2) Set

(3) Reset

(4) Toggle

(1) 10

(2) 15

(3) 25

(4) 30

**Answer : 3****2. The number of different spanning tree in complete graph, K4 and bipartite graph, K2,2, Have ______ and _______ respectively.**

(1) 14,14

(2) 16,14

(3) 16,4

(4) 14,4

**Answer : 3**3. Suppose that R1 and R2 are reflexive relations on a set A.

Which of the following statement is correct?

(1) R1 ∩ R2 is reflexive and R1 ∩ R2 is irreflexive

(2) is irreflexive and R1 ∩ R2 is reflexive

(3) Both R1 ∩ R2 and R1 ∩ R2 are reflexive

(4) Both R1 ∩ R2 and R1 ∩ R2 are irreflexive

**Answer : 3****4. There are three card in a box, Both sides of one card are black , both sides of one card are red, and the third card has one black side one red side we pick a card at random and observe only one side.**

What is the probability that the opposite side is the same color as the one side we observe?

(1)3/4

(2) 2/3

(3) ½

(4) 1/3

**Answer : 2****5. A Clique in a simple undirected graph is a complete subgraph that is not contained in any larger complete subgraph. How many clique are there in the graph shown below?**

(1) 2

(2) 4

(3) 5

(4) 6

**Answer : 3****6. Which of the following logic expressions is incorrect?**

(1) 1 Θ 0=1

(2) 1 Θ 1 Θ 1=1

(3) 1 Θ 1 Θ 0=1

(4) 1 Θ 1=0

**Answer : 3****7. The IEEE-754 double precision format to represent floating point number, has a length of _____ bits**

(1) 16

(2) 32

(3) 48

(4) 64

**Answer : 4****8. Simplified Boolean equation for the following truth table is**

(1) F=xy’+y’z

(2) F=xy’+x’y

(3) F=x’y+xz’

(4) F=x’z+xz’+xyz

**Answer : 3****9. The simplified form of Boolean equation (AB’+AB’C+AC)(A’C’+B’) is :**

(1) AB’

(2) AB’C

(3) A’B

(4) ABC

**Answer : 1****10. In a positive-edge-triggered JK flip-flop, if J and K both are high then the output will be _________ on the rising edge of the clock.**

(1) No change

(2) Set

(3) Reset

(4) Toggle

**Answer : 4**
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