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
Engineering-MathematicsPrepositional-LogicGATE 1994
Question 1 Explanation: 

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

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
Engineering-MathematicsPrepositional-LogicGATE 1995
Question 2 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 3

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
 concat(head(s), head(tail(tail(s))))
A
ac
B
bc
C
ab
D
cc
Engineering-MathematicsPrepositional-LogicGATE 1995
Question 3 Explanation: 
concat (a, head (tail (tail (acbc))))
concat (a, head (tail (cbc)))
concat (a, head (bc))
concat (a, b)
ab
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
Engineering-MathematicsPrepositional-LogicGATE 1993
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
Engineering-MathematicsPrepositional-LogicGATE 1992Video-Explanation
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
Engineering-MathematicsPrepositional-LogicGATE 1992Video-Explanation
Question 6 Explanation: 
There are 6 questions to complete.

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