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)
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 ____ _____ _______ _________ __________ _______ __________ _________ _____ ____.
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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.
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
Evaluate
y=sin3 x cos3 x
For the statement p and q, consider the following compound statements:
B. {(pvq)^-p} → q
Then which of the following statement is correct:
(i) A is a tautology but not B
(ii) A and B both are not tautologies
(iii) A and B both are tautologies
(iv) B is a tautology but not A
If x,y,z be respectively the pth, qth and rth term of G.P., then evaluate
(q-r) logx + (r-p) logy + (p-q) logz