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Cardinality of Sets

If A =[1,2,3]...

Question

If A = [1, 2, 3], B = [4, 5, 6], which of the following are relations from A to B? Give reasons in support of your answer.

(i) [(1, 6), (3, 4), (5, 2)]
(ii) [(1, 5), (2, 6), (3, 4), (3, 6)]
(iii) [(4, 2), (4, 3), (5, 1)]
(iv) A × B.

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Solution

Given:
A = {1, 2, 3} and B = {4, 5, 6}
Thus, we have:
A × B = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)}

(i) {(1, 6), (3, 4), (5, 2)}
Since it is not a subset of A × B, it is not a relation from A to B.
(ii) {(1, 5), (2, 6), (3, 4), (3, 6)}
Since it is a subset of A × B, it is a relation from A to B.
(iii) {(4, 2), (4, 3), (5, 1)}
Since it is not a subset of A × B, it is not a relation from A to B.
(iv) A × B
Since it is a subset (equal to) of A × B, it is a relation from A to B.

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Similar questions

If A = {1, 2, 3}, B = {4, 5, 6} which of the following are relations from A to B ?

Give reasons in support of your answer.

(i) {(1, 6), (3, 4), (5, 2)}

(ii) {(1, 5), (2, 6), (3, 4), (3, 6)}

(iii) {(4, 2), (4, 3), (5, 1)}

(iv) $A \times B$ .

A = {1, 2, 3}

B = {4, 5, 6}

A

B

R_{1} = {(4, 2) (2, 6) (5, 1) (2, 4)}

R_{2} = {(1, 4) (1, 5) (3, 6) (2, 6) (3, 4)}

R_{3} = {(1, 5) (2, 4) (3, 6)}

R_{4} = {(1, 4) (1, 5) (1, 6)}

A \subseteq B or B \subseteq A;

Which of the following statements are true ? Give reason to support your answer.

(i) For any two sets A and B either A $\subseteq$ B or B $\subseteq$ A.

(ii) Every subset of an infinite set is infinite.

(iii) Every subset of a finite set is finite.

(iv) Every set has a proper subset.

(v) {a,b,a,b,a,b....} is an infinite set.

(vi) {a, b, c} and {1, 2, 3} are equivalent sets.

(vii) A set can have infinitely many subsets.

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