1. The Boolean function [~(~p ∧ q) ∧ ~( ~p ∧ ~q)] ∨ (p ∧ r)] is equal to the Boolean function:

- Option : D
- Explanation :

We have Boolean function: [~(~p ∧ q) ∧ ~( ~p ∧ ~q)] ∨ (p ∧ r)] = [(p ∨ ~q) ∧ (p ∨ q ) ∨ (p ∧ r)] = [p ∨ (p ∧ q) ∨ (p ∧ ~q) ∨(p ∧ r)] = p[1 ∨ q ∨ ~q ∨ r] = p So, option (D) is correct.

You must be logged in to post a comment.

- Option : B
- Explanation :

We have compound proposition (~ (p ∧ q)) ↔ (~ p ∨ ~ q): Now we will construct ordered tree:

We are asked to determine pre-order (i.e. parent-node left-node right-node), we will drive it from ordered tree i.e. ↔ ~ ∧ p q ∨ ~ p ~q And post-order(i.e. left-node right-node parent-node) from the ordered tree it is p q ∧ ~ p ~ q ~ ∨ ↔. So, option (B) is correct.

You must be logged in to post a comment.

You must be logged in to post a comment.

4. What is the probability that a randomly selected bit string of length 10 is a palindrome?

- Option : B
- Explanation :

In the given question we have a palindrome: in even length palindrome half length is fixed and rest is repeated. So, in 10 bit palindrome, we have 5 position to be filled with 2 choices each-

i.e. 2^{5}choices for first half and 2^{5}choices for second half.

Probability = favorable outcome / total outcome

= 2^{5}/ 2^{10}

= 1 / 2^{5}

= 1 / 32.

So, option (B) is correct.

You must be logged in to post a comment.

You must be logged in to post a comment.

5. Given the following graphs:

Which of the following is correct?

- Option : C
- Explanation :

Euler circuit does not contain odd length cycle. Refer: Eulerian path and circuit for undirected graph None of the above graph is Eulerian. So, option (C) is correct.

You must be logged in to post a comment.

You must be logged in to post a comment.

You must be logged in to post a comment.