Let T be a relation from A = {0, 1, 2, 3} to B = {0, 1, 2, 3, 4} such that (a, b) ∈ T iff b2 – a2 is an odd number. (A, B ⊆ U = Z.)(Hint: Write down all the elements of T. For example, if 4 ∈ B and 1 ∈ A then 42 – 12 = 16 – 1 = 15 which is an odd number, thus (1, 4) ∈ T.)Which one of the following statements regarding the relation T is true?a.T is transitive.b.T is symmetric.c.T is antisymmetric.d.T is irreflexive.

Let R be the relation on Z≥ (the set of integers) defined by (x, y) ∈ R iff x2 + y2 = 2k for some integers k ≥0.Which one of the following is an ordered pair in R?a.(1, 0)b.(2, 9)c.(3, 8)d.(5, 7)

Let the set 𝐴={1,2,3,4}. and consider the following relations on the set A R={(1,1),(2,2),(3,3),(4,4)} S={(1,2),(2,1),(3,4),(4,3), (3,3)} T={(1,2),(2,3),(1,3), (4,4)} U={(1,3),(2,4),(3,1),(4,2),(1,1),(1,4)}then:R is and  and S is and  and T is and  and U is and  and

Q1. Let 𝐴 = {0,1,2,3,4,5,6,7} suppose 𝑅 𝑎𝑛𝑑 𝑇 are two relations on 𝐴 such that 𝑅 = {(𝑥, 𝑦): 𝑥 + 2𝑦 ≥ 4}, 𝑇 = {(𝑥, 𝑦): 2𝑥 + 3𝑦 ∈ 𝐴} Write 𝑅, 𝑇, 𝑎𝑛𝑑 𝑅°𝑇 pls solve it find R and t

For each of the following relations defined on sets M = {5, 6, 7, 8} and N = {1, 3, 5, 7, 9},list the elements and find its domain and range.(a) S1 = {(m, n)|m + n is even}(b) S2 = {(m, n)|n = 2m − 9}(c) S3 = {(m, n)|m < n}(d) S4 = {(m, n)||m − n| ≤ 2}(e) S5 = {(m, n)|m is divisible by n}(f) S6 = {(m, n)|m + n is a prime number

For each of the following relations defined on sets M = {5, 6, 7, 8} and N = {1, 3, 5, 7, 9},list the elements and find its domain and range.(a) S1 = {(m, n)|m + n is even}(b) S2 = {(m, n)|n = 2m − 9}(c) S3 = {(m, n)|m < n}(d) S4 = {(m, n)||m − n| ≤ 2}(e) S5 = {(m, n)|m is divisible by n}(f) S6 = {(m, n)|m + n is a prime number}