Consider the following sets, where \(n≥2\): \(S_1\): Set of all \(n×n\)…

GATE · 2021 · CS · Set 2 · Computer Science & IT

Consider the following sets, where n≥2n≥2:

S1S_1: Set of all n×nn×n matrices with entries from the set {a,b,c}\{a,b,c\}

S2S_2: Set of all functions from the set 0,1,2...,n2−1 {0,1,2 ... ,n^2−1} to the set {0,1,2}\{0,1,2\}

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

  1. A.

    There does not exist a bijection from S1S_1 to S2S_2.

  2. B.

    There exists a surjection from S1S_1 to S2S_2.

  3. C.

    There exists a bijection from S1S_1 to S2S_2.

  4. D.

    There does not exist an injection from S1S_1 to S2S_2.

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