You visited us 1 times! Enjoying our articles? Unlock Full Access!

Cartesian Product

If A= a,b,c...

Question

If $A = {a, b, c, d}, B = {1, 2, 3}$ find whether or not the following sets of ordered pairs are relations from $A$ to $B$ or not.
$R_{1} = {(a, 1), (a, 3)}$
$R_{2} = {(a, 1), (c, 2), (d, 1)}$
$R_{3} = {(a, 1), (b, 2), (3, c)} .$

R_{1}

R_{2}

are relations but

R_{3}

is not a relation.

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

R_{1}

R_{3}

are relations but

R_{2}

is not a relation.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

All are relations

No worries! We‘ve got your back. Try BYJU‘S free classes today!

none of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $R_{1}$ $R_{2}$ are relations but $R_{3}$ is not a relation.
Given, $A = {a, b, c, d}, B = {1, 2, 3}$ and
$R_{1} = {(a, 1), (a, 3)}$
$R_{2} = {(a, 1), (c, 2), (d, 1)}$
$R_{3} = {(a, 1), (b, 2), (3, c)} .$
We know that every relation from $A$ to $B$ will be a subset of $A \times B$ .
Thus, both $R_{1}$ and $R_{2}$ are subsets of $A \times B$ and hence are relations but $R_{3}$ is not a relation because $R_{3}$ is not a subset of $A \times B$ because the element $(3, c) \notin (A \times B) .$ It belongs to $B \times A .$

Suggest Corrections

Similar questions

R_{1}

R_{2}

R_{3}

R = {(a, a), (b, c), (a, b)}

A = {a, b, c} .

A = {1, 2, 3, 4, 5}, B = {1, 3, 5, 7, 9, 10, 17, 26, 30}

R_{1} = {(1, 3), (3, 3), (5, 17), (1, 2)}

R_{2} = {(3, 7), (4, 5), (5, 30)}

R_{3} = {(x, y) : x ϵ A, y ϵ B, x + y = 8}

R_{4} = {(x, y) : x ϵ A, y ϵ B, y = x^{2} + 1}

R_{5} = {(x, y) : x ϵ A, y ϵ B, y = 2 x - 1}

A

B

A \times B

6

A \times B

(1, 4), (2, 6), (3, 6)

B \times A

= {(a, 1), (6, 1), (4, d), (c, 2), (4, 3) (b, 3)}

a + b + c + d

Join BYJU'S Learning Program