If R is a relation from a set P to set Q, then *
(a) R ⊆ P × Q
(b) R ⊆ Q × P
(c) R = P ×Q
(d) R = P U Q
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Answer:
From then definiation of Relation
Let R be a relation from A to B
i.e., R⊆A×B, then
Domain of {a:a∈A,(a,b)∈R for some b∈B}
Range of R={ b:b∈B,(a,b)∈R for some a∈A}.
Therefore,
(A) R,={(a,p),(b,s),(c,s)} is a relation as {a,b,c}⊆A and {p,r,s}⊆B.
(B) R2={(q,b),(c,s),(d,r)} is not a relation as q is not from set A.
(C) R3={(a,p),(a,q),(d,p),(c,r),(b,r)} is a relation as {a,d,c,b}⊆A and {p,q,r}⊆B.
(D)R4={(a,p),(q,a),(b,s),(s,b)} is not a relation as q and s does not belong to set A.
Step-by-step explanation:
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