1
GATE CSE 2021 Set 2
Numerical
+2
-0

Consider a Boolean function f(w, x, y, z) such that 

f(w, 0, 0, z) = 1

f(1, x, 1, z) = x + z

f(w, 1, y, z) = wz + y

The number of literals in the minimal sum-of-products expression of f is ______

Your input ____
2
GATE CSE 2021 Set 2
MCQ (More than One Correct Answer)
+1
-0

Consider the following sets, where n > 2:
S1: Set of all n x n matrices with entries from the set {a, b, c}

S2: Set of all functions from the set {0,1, 2, ..., n2 — 1} to the set {0, 1, 2}

Which of the following choice(s) is/are correct?

A
There does not exist an injection from S1 to S2.
B
There exists a bijection from S1 to S2
C
There exists a surjection from S1 to S2.
D
There does not exist a bijection from S1 to S2
3
GATE CSE 2021 Set 2
MCQ (More than One Correct Answer)
+1
-0

Choose the correct choice(s) regarding the following propositional logic assertion S:

S : ((P ∧ Q)→ R)→ ((P ∧ Q)→ (Q → R))

A
The antecedent of S is logically equivalent to the consequent of S.
B
S is a tautology
C
S is a contradiction
D
S is neither a tautology nor a contradiction.
4
GATE CSE 2021 Set 2
Numerical
+1
-0
Suppose that f : R → R is a continuous function on the interval [-3, 3] and a differentiable function in the interval (-3, 3) such that for every x in the interval, f'(x) ≤ 2. If f(-3) = 7, then f(3) is at most _______.
Your input ____