1. State
whether the following sentence is statement in logic. Justify your answer.

a. The square
of any odd integers is even.

b. 5 + 4 = 11

2. Express
the following statements in symbolic form:

a. It is
raining and cold.

b. Sachin
Tendulkar scored double century or India won the match.

3. Write the
truth value of the following statements:

a. Paris is
in China or London is in Germany.

b. 2 + 3 = 5
or 3 < 0.

4. Write the
negations of the following statements:

a. ABCD is a
quadrilateral

b. 3 is a
rational number.

5. Using the
statements p : Seema is fat, q : Seema
is happy. Write the following statements in the symbolic form.

a. Seema is
thin but happy.

b. It is not
true that if Seema is happy then she is not fat.

6. If A = {2,
3, 4, 5, 6, 7, 8}, determine the truth value of each of the following:

a. ヨx
∈ A, such that x +
5 = 8

b. ∀x ∈ A, x + 1 ≤ 10.

7. Use
quantifiers to convert each of the following open sentences defined on N, into
a true statement:

a. X

^{2}+ 1 = 26.
b. 3x + 1 ≤ 5

8. Examine
whether each of the following statement patterns is a tautology or a
contradiction of a contingency.

a. [(p➝ q) ⋀
(~ q) ] ➝
(~p)

b. [ p ➝ (~ q V r) ] ↔ ~
[ p ➝
( q ➝
r )]

9. Write the
dual of each of the following:

a. ( p ⋀
q ) ⋀
r.

b. Madhu is
fair and Mahesh is intelligent.

10. Write the
following statements is symbolic form and write their negations.

a. x + 3 <
5 or y + 5 = 9

b. 7 > 2
and 3 > 10.