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GATE | GATE CS 2021 | Set 2 | Question 21
• Last Updated : 23 May, 2021

Consider the following sets, where n≥2:

• S1: Set of all n×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 a bijection from S1 to S2
(B) There exists a surjection from S1 to S2
(C) There exists a bijection from S1 to S2
(D) There does not exist an injection from S1 to S2

Explanation:

S1: We know that there are n×n positions in matrix each can be filled with either a or b or c so total we have 3^n×n ways

S2: Total number of functions possible from A to B is (Cardinality of B)^Cardinality of A

For ex- |B|= 3 and |A|= n^2-1 +1 = n^2. So in this case total functions possible is 3^n×n

So the function is Surjective as well as Bijective Correct Option- B, C

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