Find all functions from A to B Consider a function F 2 16 1

Find all functions from A to B? Consider a function F = (((-2, 16), (-1, 9), (0, 4), (1, 4), (2, 9), (3, 16), (4, 1))) What is the domain of F? {-2, -1, 0, 1, 2, 3} {1, 4, 9. 16} {-2, -1, 0, 1, 2, 3, 4, 9, 16} {1, 4} What is the range of F? [1, 4] {1, 4, 9} {-1, 0, 2, 4} {1, 4} find the inverse image of (4, 9) under F? {-2, -1, 0, 1, 2, 3} {-1, 0, 1, 4} {-2, -1, 0, 1, 2, 3, 4, 9, 16} The congruence modulo 4 relation on Z, that is, For all integers m and n, m C n if and only if 4|(m - n), which is true? 4C2 7C0 5C - 1 -6C2 none of the above Let X = {-2, 0, 1, 2, 3} and Y = {0, 2, 4, 6, 8}. We define a function F:X rightarrow Y as F = {(-2, 0}, {0, 6), (1, 4), (2, 2), (3, 6)}. Is F one-to-one or onto? Only one-to-one Only onto one-to-one and onto The congruence modulo relation on Z, which is true? 12 7 (mod 4) 12 7 (mod 4) -11 7 (mod 2) 6 -8 (mod 3) Let R be the relation of congruence modulo 5. Which of the following equivalence classes do equal to [1]? [-4] [-17] [-13] [-6] none of these

Solution

17. a and d are functions , b is not a function because first element is mapped to two elements inthe codomain or B. c is not a function because domain one element is having any image in B

18. the domain is the x cordinate of the (x,y) pair you see there

so we have answer as none of these because the actual domain is {-2,-1,0,1,2,3,4}

19. range of F is {16,9,4,1} which is option B

20 the image is {4,9,1} that is option B

21 {0,1,-1,2} that is option d

22. c is correct because -11 is congruent to 7mod2 or -18 is congruent to 0 mod2 which is true i.e when you dvide -18 by 2 you get remainder 0

23. d is correct since 4|(-6-2) or 4|(-8) i.e 4 divides -8

24. the option is a that is it is one one (but not onto since the element 8 has no preimage in A)