LOGIC TEST PAPER JUNE 16

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. 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. X2 + 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.


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