8. A={1,2,3,4} and B={a,b,c,d} be two sets. Choose which of the followings are relation from A to B - Advance Math Class 10 - Exercise 1.3

Related Quarries: let a= a b c and b= 1 2 3 4 then the number of elements, let a=(1,2,3 and b=(a,b,c,d then the number of relation from a to b is)), if a=(1,2,3 b=(a,b, c which of the following is are relation s from a to b)), let a a b c d and b = (1, 2, 3 which of the following relations from a to b is not a function), state which of the following is the total number of relations from the set a a b c to b d e, let a= 1 2 3 4 and b= 2 4 6, 2/3,4/9 o f 3/5 1 2/3 1 1/4 - 1/3, let a= 1 2 3 4 and b= a 0 0 b.

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Solution:

Given, 

B = {a, b, c, d}

A x B = {(1, a),(1, b), (1, c), (1, d), (2, b), (2, c), (2, d), (3, a),(3, b), (3, c), (3, d), (4, a),(4, b), (4, c), (4, d)}

(i) {(1, a), (1, b), (2, c), (4, d)}

Answer: Yes, this is a relation from A to B, because all the order pairs belongs to A x B.

(ii) {(1, 1), (1, a), (3, c)}

Answer: No, this is not a relation from A to B, because (1, 1) does not belongs to A x B.

(iii) A x B

Answer: Yes, this is a relation from A to B, because all the order pairs belongs to A x B.

(iv) {(a, 1), (b, 2), (c, 3)}

Answer: No, this is not a relation from A to B, because (a, 1), (b, 2), (c, 3) does not belongs to A x B.

(v) { ϕ }

Answer: No, this is not a relation from A to B, because { ϕ } does not belongs to A x B.

(vi){(1, c), (2, c), (3, c), (4, c)}

Answer: Yes, this is a relation from A to B, because all the order pairs belongs to A x B.

Exercise: 1.3

1. If A = {1, 3}, then write the identity relation I : A⟶A. Also write the universal relation on A ?

2. If A = {1, 2} then write down all the relation on A ?

3. If A = (1, 2, 3) then find the elements of the relation R= {(x, y): x=y and x, y Є A} on A ?

4. Z + is the set of positive integers and R: Z+ → Z+ is a relation defined as R = {(a, b) | a, b Є Z+ and a-b >2}. Is it a finite relation? Represent R as a set in the Roster form ?

5. A={2,3,4,5} and B={3,6,7,10} be two sets and a relation R is defined as R={(x, y): x completely divides y where x Є A and y Є B}. Write the relation R in the tabular form. Also represent R by arrow diagram and matrix table ?

6. Determine R^-1 of the relation R given in question 5 above. Also find d(R^-1) and r(R^-1) ?

7. A={3,6,8,9} is a set and aRb iff a-b is divisible by 3 for a,b Є A. Then (i) Write R as a set and draw the arrow diagram. (ii) Find d(R) and r(R). (iii) Can we find the inverse of R ?

8. A={1,2,3,4} and B={a,b,c,d} be two sets. Choose which of the followings are relation from A to B ?

9. A relation R is defined on the the set of natural N as aRb where a=b^2 for a,bЄN. Write the relation R. Also write R^-1 in set builder method ?

10. If A={1,2,3,4,6} and R is a relation on A defined as R={(x,y):y is exactly divisible by x where x,yЄA} then ?

11. Let A = {10, 11, 12, 13} and B = {1, 2, 3, 4} be two sets. Write the following relations from A to B as defined in each case ?

12. R1 and R2 be two relations on the set of integers Z defined as below -(i) R1={(a,b):a^2=b^2 and a,b∈Z} (ii) R2={(a,b): a-b is positive where a,b are primes and both are smaller than 10} determine the domain and the range of each of them ?