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Range

Let A = a 1, ...

Question

Let A={a1,a2,a3,a4,a5} and B={b1,b2,b3,b4,} where ai's and bi's are school going students . Define a relation from A to B by xRy iff y is a true friend of x . If R={(a1,b1),(a2,b1),(a3,b3),(a4,b2},(a5,b2)} . Prove that R is neither one one nor onto

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Solution

Since (a1,b1),(a2,b1) are present in R, it means b1 is related to both a1 and a2. This means it is many one since many are related to one in the co domain.
since the range of R consists of only {b1,b2,b3} and since codomain has b4 and b4 more, it means R is not onto but into.

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Similar questions

Let A={a1,a2,a3,a4,a5} and B={b1,b2,b3,b4,b5} where ai's and bi's are school going students . Define a relation from A to B by xRy iff y is a true friend of x . If R={(a1,b1),(a2,b2),(a3,b3),(a4,b4),(a5,b5)} . Prove that R is neither one one nor onto

Q. Suppose four distinct positive number

a_{1}, a_{2}, a_{3}, a_{4}

are in G.P. Let

b_{1} = a_{1}, b_{2} = b_{1} + a_{2}, a_{3} = b_{2} + a_{3}

b_{4} = b_{3} + a_{4}

Statement 1 - The numbers

b_{1}, b_{2}, b_{3}, b_{4}

are neither in A.P. nor in G.P.
Statement 2 - The numaber

b_{1}, b_{2}, b_{3}, b_{4}

Q. Suppose four distinct positive numbers

a_{1}, a_{2}, a_{3}, a_{4}

G . P

b_{1} = a_{1}, b_{2} = b_{1} + a_{2}, b_{3} = b_{2} + a_{3}

b_{4} = b_{3} + a_{4}

.
STATEMENT-1 : The numbers

b_{1}, b_{2}, b_{3}, b_{4}

A . P

G . P

.
STATEMENT-2 : The numbers

b_{1}, b_{2}, b_{3}, b_{4}

H . P

.

Q. Assertion :Suppose four distinct positive numbers

a_{1}, a_{2}, a_{3}, a_{4}

b_{1} = a_{1}, b_{2} = b_{1} + a_{2}, b_{3} = b_{2} + a_{3}

b_{4} = b_{3} + a_{4} .

STATEMENT- 1: The numbers

b_{1}, b_{2}, b_{3}, b_{4}

are neither in AP nor in GP, and Reason: STATEMENT- 1: The numbers

b_{1}, b_{2}, b_{3}, b_{4}

2 y - x = 8; 5 y - x = 14, y - 2 x = 1

(a_{1}, b_{1}), (a_{2}, b_{2}), (a_{3}, b_{3})

(a_{1} + a_{2} + a_{3} + b_{1} + b_{2} + b_{3})

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