## Prepositional-Logic

 Question 1

Let p and q be propositions. Using only the truth table decide whether p ⇔ q does not imply p → q is true or false.

 A True B False
Question 1 Explanation:

So, "imply" is False making "does not imply" True.
 Question 2

A language with string manipulation facilities uses the following operations

``` head(s): first character of a string
tail(s): all but the first character of a string
concat(s1,s2):s1 s2
for the string acbc what will be the output of
 A ac B bc C ab D cc
Question 2 Explanation:
concat (a, head (tail (tail (acbc))))
concat (a, b)
ab
 Question 3

If the proposition ¬p ⇒ ν is true, then the truth value of the proposition ¬p ∨ (p ⇒ q), where ¬ is negation, ‘∨’ is inclusive or and ⇒ is implication, is

 A true B multiple valued C false D cannot be determined
Question 3 Explanation:
From the axiom ¬p → q, we can conclude that p ∨ q.
So, either p or q must be True.
Now,
¬p ∨ (p → q)
= ¬p ∨ (¬p ∨ q)
= ¬p ∨ q
Since nothing c an be said about the truth values of p, it implies that ¬p ∨ q can also be True or False. Hence, the value cannot be determined.
 Question 4

The proposition p ∧(~p ∨ q) is:

 A a tautology B logically equivalent to p ∧ q C logically equivalent to p ∨ q D a contradiction E none of the above
Question 4 Explanation:
p ∧(~p ∨ q)
(p ∧ ~p) ∨ (p ∧ q)
F ∨ (p ∧ q)
(p ∧ q)
 Question 5
Which of the following predicate calculus statements is/are valid:
 A a B b C c D d
Question 5 Explanation:
(A) Valid
(B) Invalid
(C) Invalid
(D) Invalid
 Question 6
Which of the following is/are tautology
 A a B b C c D d
Question 6 Explanation:
There are 6 questions to complete.

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