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Definition of Relations

If A= 1,2,3...

Question

If $A = {1, 2, 3}$ and $B = {4, 5, 6}$ then which of the following sets are relation from $A$ to $B$
(i) $R_{1} = {(4, 2) (2, 6) (5, 1) (2, 4)}$
(ii) $R_{2} = {(1, 4) (1, 5) (3, 6) (2, 6) (3, 4)}$
(iii) $R_{3} = {(1, 5) (2, 4) (3, 6)}$
(iv) $R_{4} = {(1, 4) (1, 5) (1, 6)}$

R_{1}, R_{2}, R_{3}

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R_{1}, R_{3}, R_{4}

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R_{2}, R_{3}, R_{4}

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R_{1}, R_{2}, R_{3}, R_{4}

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Solution

The correct option is B $R_{2}, R_{3}, R_{4}$
A relation from $A$ to $B$ will include elements from $A \times B$
Elements of $A \times B$ are
${(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)}$
Now the relation $R_{1}$ consists of elements form both $A \times B$ and $B \times A$ .
Thus $R_{1}$ is not a relation from $A$ to $B .$

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R_{5}

f (x) = 4 x^{4} - a x^{3} + b x^{2} - c x + 5

(a, b, c ϵ R)

r_{1}, r_{2}, r_{3}, r_{4}

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