Question
Which of the following Boolean expression is a tautology?
(i) (p^q) v (pvq)
(ii) (p^q) v (p→q)
(iii) (p^q) ^ (p→q)
(iv) (p^q) → (p→q)
Answer :
Word Count : 573
A tautology is a Boolean expression that is always true regardless of the truth values of the variables involved. Let's analyze each of the given expressions using a truth table. ### Step 1: Define the Variables We have two Boolean variables: - \( p \) (can be T or F) - \( q \) (can be T or F) We will construct a truth table and evaluate each given expression. | \( p \) | \( q \) | \( p \to q \) | \( p \land q \) | \( p \lor q ______ __________ ______ ____ _____ _________ ____ _____ _______ _________.
_____ _______ ________ _______ ___ _________.
___ _________ _______ __________ ___ _______.
_____ __________ _____ ___ _________ ________ _____ _____ ______.
_________ _________ _________ _________ _____ __________ _______ _______ ____ _____.
______ ______ ____ _____ _____ _________.
__________ _________ _________ ________ __________ ____ ___ _________ _________ _____.
_________ ______ __________ ___ ____ ______ ________.
______ ___ ____ ________ __________ _____ ______.
_____ _______ ______ ________ __________ ______ ___ _____ __________.
____ _______ __________ ___ _____ __________ __________.
_______ _________ ________ _______ ___.
_____ _______ ___ ________ _________ __________.
____ _______ ____ _____ ______ _____ ____ _____ ___.
___ _____ ________ _______ ____ _______.
_____ ____ __________ _______ ________ ________ _______ ________ __________.
_____ _________ __________ ______ _____ _______ _____ _________ __________.
__________ ____ ________ ___ __________ ____ __________ __________ _________ ________ _____.
_______ ___ ___ __________ _________.
_______ _________ __________ ____ ______ _________.
______ _______ _________ _______ ______ __________ ___ _____.
_________ _______ ____ ____ ________ __________.
___ ______ ____ _____ ___ _____ ________.
_____ ___ _____ _________ ____.
_______ _________ __________ ___ ___ ________ __________ ________ ________ ___ ______.
_____ _____ ______ __________ __________ ____ _____.
_________ _________ __________ ______ _____ __________ ______ ______ _______ _________.
____ ___ __________ _________ ______ ______ __________ ____ ______.
______ _____ ___ ______ _________ _____ _____ _____.
________ _________ __________ _____ _______ _______ __________ _____ ________ _________ ___ ________.
____ __________ _________ __________ _________ _____ __________ __________ ______ ____ _______.
______ ___ ___ _______ ___.
________ ___ ______ _____ ________ ___ ______ ______ ____ _______ ________ ____.
__________ _____ ______ ___ _____ _______ __________.
________ ______ _______ ________ ___ ______ __________ ____ _____ ___.
_______ __________ ________ _________ ______ ___ _______ _________ ____.
_________ ________ _____ _________ __________ _____ ________.
______ ________ ________ ______ _______ __________ __________ _____ _______ _____ __________ ________.
___ __________ ______ _______ ________ ___ ___ __________ ______ ___.
___ ________ _______ ____ ________ ________ ________.
___ _________ _______ ________ _______ ________ ___ _________ ____ ___.
______ ______ ___ _______ ____ __________.
____ ____ _________ __________ _____ _____ __________ ___.
____ _______ ______ __________ ____ ______ ________ ____ _____ ___ _______ _______.
_______ ______ __________ ___ ____ _________ ______ ______ _________ _____ _______ _____.
______ ____ ______ _______ _________.
____ __________ _______ ____ ____ ____ ___ _______ ________ _____ ____ _______.
__________ _________ _____ ________ _______ _____ ___ ____ _______.
_________ _____ ___ __________ __________ ____ __________.
__________ ____ ________ ________ ________ __________.
___ ________ ________ ______ _______ ____ ___ _____.
__________ __________ _____ _______ ________ ___ ___ ____.
__________ _______ _________ ________ ______ _______ ______ ___ ______ ___ _______ ____.
_____ ______ ______ ____ _________ ___ __________.
______ __________ ________ _________ ________ ___ __________ ________ ________ _____ _________ ______.
___ ___ __________ _____ _______ _________ ________ ________ ______ ______.
_______ ______ ___ ________ ________ _________.
____ __________.
Get Full Answer on WhatsApp
A tautology is a Boolean expression that is always true regardless of the truth values of the variables involved. Let's analyze each of the given expressions using a truth table. ### Step 1: Define the Variables We have two Boolean variables: - \( p \) (can be T or F) - \( q \) (can be T or F) We will construct a truth table and evaluate each given expression. | \( p \) | \( q \) | \( p \to q \) | \( p \land q \) | \( p \lor q ______ __________ ______ ____ _____ _________ ____ _____ _______ _________.
_____ _______ ________ _______ ___ _________.
___ _________ _______ __________ ___ _______.
_____ __________ _____ ___ _________ ________ _____ _____ ______.
_________ _________ _________ _________ _____ __________ _______ _______ ____ _____.
______ ______ ____ _____ _____ _________.
__________ _________ _________ ________ __________ ____ ___ _________ _________ _____.
_________ ______ __________ ___ ____ ______ ________.
______ ___ ____ ________ __________ _____ ______.
_____ _______ ______ ________ __________ ______ ___ _____ __________.
____ _______ __________ ___ _____ __________ __________.
_______ _________ ________ _______ ___.
_____ _______ ___ ________ _________ __________.
____ _______ ____ _____ ______ _____ ____ _____ ___.
___ _____ ________ _______ ____ _______.
_____ ____ __________ _______ ________ ________ _______ ________ __________.
_____ _________ __________ ______ _____ _______ _____ _________ __________.
__________ ____ ________ ___ __________ ____ __________ __________ _________ ________ _____.
_______ ___ ___ __________ _________.
_______ _________ __________ ____ ______ _________.
______ _______ _________ _______ ______ __________ ___ _____.
_________ _______ ____ ____ ________ __________.
___ ______ ____ _____ ___ _____ ________.
_____ ___ _____ _________ ____.
_______ _________ __________ ___ ___ ________ __________ ________ ________ ___ ______.
_____ _____ ______ __________ __________ ____ _____.
_________ _________ __________ ______ _____ __________ ______ ______ _______ _________.
____ ___ __________ _________ ______ ______ __________ ____ ______.
______ _____ ___ ______ _________ _____ _____ _____.
________ _________ __________ _____ _______ _______ __________ _____ ________ _________ ___ ________.
____ __________ _________ __________ _________ _____ __________ __________ ______ ____ _______.
______ ___ ___ _______ ___.
________ ___ ______ _____ ________ ___ ______ ______ ____ _______ ________ ____.
__________ _____ ______ ___ _____ _______ __________.
________ ______ _______ ________ ___ ______ __________ ____ _____ ___.
_______ __________ ________ _________ ______ ___ _______ _________ ____.
_________ ________ _____ _________ __________ _____ ________.
______ ________ ________ ______ _______ __________ __________ _____ _______ _____ __________ ________.
___ __________ ______ _______ ________ ___ ___ __________ ______ ___.
___ ________ _______ ____ ________ ________ ________.
___ _________ _______ ________ _______ ________ ___ _________ ____ ___.
______ ______ ___ _______ ____ __________.
____ ____ _________ __________ _____ _____ __________ ___.
____ _______ ______ __________ ____ ______ ________ ____ _____ ___ _______ _______.
_______ ______ __________ ___ ____ _________ ______ ______ _________ _____ _______ _____.
______ ____ ______ _______ _________.
____ __________ _______ ____ ____ ____ ___ _______ ________ _____ ____ _______.
__________ _________ _____ ________ _______ _____ ___ ____ _______.
_________ _____ ___ __________ __________ ____ __________.
__________ ____ ________ ________ ________ __________.
___ ________ ________ ______ _______ ____ ___ _____.
__________ __________ _____ _______ ________ ___ ___ ____.
__________ _______ _________ ________ ______ _______ ______ ___ ______ ___ _______ ____.
_____ ______ ______ ____ _________ ___ __________.
______ __________ ________ _________ ________ ___ __________ ________ ________ _____ _________ ______.
___ ___ __________ _____ _______ _________ ________ ________ ______ ______.
_______ ______ ___ ________ ________ _________.
____ __________.
Get Full Answer on WhatsApp
Related Questions
State whether the following statement are True or False and also give the reason in support of your answer.
a) Collection of intelligent students of IGNOU forms a set.
b) Following rule is a function from A to B
c)
d) The negation of the following statement p is-p.
p: Longest chord of a circle is diameter -p: Diameter is the shortest chord of circle
e) Any term of an AP(except the first and last) is equal to half the sum of terms which are equidistant from it on both sides
If the universal set is U = {1,2,3,4,5,6,7,9,10) and A= {2,3,6,7}, B= {4,6,8,9}, C= {6,7,8} are the subsets of U, then verify
a) De-Morgan's Laws
b) Left distributive law
Evaluate
Evaluate
The numbers a,b and c are between 2 and 18, such that, (i) their sum is 25, (ii) the number 2, a and b are consecutive terms of an A.P. and (iii) the number b,c and 18 are consecutive terms of a G.P. Find the values of a,b,c.
IGNOU NEWS
Assignment Submission Last Date Extended Till 30 June 2026 Click Here★★★IGNOU June 2026 TEE Date Sheet Released Click Here★★★