Let A=1,2,3,4,5, B=1,3,5,7,9,10,17,26,30. Which of the following sets of ordered pairs are (i) relations (ii) functions (iii) neither, from A to B (a) R1= {(1, 3), (3, 3), (5, 17), (1, 2)}(b) R2 = {(3, 7), (4, 5), ( 5, 30)}(c) R3=(x,y):x∈A,y∈B,x+y=8(d) R4=(x,y):x∈A,y∈B,y=x2+1(e) R5=(x,y):x∈A,y∈B,y=2x−1

Question

Let A=1,2,3,4,5, B=1,3,5,7,9,10,17,26,30. Which of the following sets of ordered pairs are (i) relations (ii) functions (iii) neither, from A to B (a) R1​= {(1, 3), (3, 3), (5, 17), (1, 2)}(b) R2​ = {(3, 7), (4, 5), ( 5, 30)}(c) R3​=(x,y):x∈A,y∈B,x+y=8(d) R4​=(x,y):x∈A,y∈B,y=x2+1(e) R5​=(x,y):x∈A,y∈B,y=2x−1

Filo · Accepted Answer

R1​ neqR as (1,2)∈/A×B,R1​=f as 2 or 4 ∈ A has no image in B, R2​=R but R2​=f as in R1​R3​=(1,7),(3,5),(5,3)x+y=8,x∈A,y∈B∴R3​ = R being a subset ofA×B but R3​=f as in R1​ R4​=(2,5),(3,10),(4,17),(5,26)∵y=x2+1,x∈A,y∈BR4​=R but R4​=f as in R1​ R5​ =(1,1),(2,3),(3,5),(4,7),(5,9)y=2x−1R5​ = R and R5​=fas each element ∈A has a unique image in B.

Question Text	Let $A = 1, 2, 3, 4, 5$ , $B = 1, 3, 5, 7, 9, 10, 17, 26, 30 .$ Which of the following sets of ordered pairs are (i) relations (ii) functions (iii) neither, from A to B (a) $R_{1}$ = {(1, 3), (3, 3), (5, 17), (1, 2)} (b) $R_{2}$ = {(3, 7), (4, 5), ( 5, 30)} (c) $R_{3} = (x, y) : x \in A, y \in B, x + y = 8$ (d) $R_{4} = (x, y) : x \in A, y \in B, y = x^{2} + 1$ (e) $R_{5} = (x, y) : x \in A, y \in B, y = 2 x - 1$
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