NO NEED EXPLANATION JUST ANSWER ONLY TY.

The TOPIC is SET, RELATIONS, AND FUNCTIONS.

1. Consider the following relations on A = {t,u,v,w). Determine whether these relations are reflexive, symmetric, anti- symmetric and transitive. 1. R1 = {(t,t), (t,u), (u,t), (u,u), (v,w), (w,t), (w, w)} 2. Rz = ((t,t), (t,u), (u,t) } 3. Rs = {(t,t), (t,u), (t,w), (u,t), (u,u), (v,v), (w,t), (w,w)} 4. R4 = {(u,t), (v,t), (w, t), (w, u), (w,v)} 5. Rs = {(t,t), (t, u), (t, v), (t, w), (u,u), (u, v), (u, w), (v,v), (v, w), (w,w)] Il. Let R and S be a relations from set A to set B given that A =(2,4,6) and B = {t, u,v,w}. R = {(2,t), (2,u), (2.v), (4,t), (4, w), (6,u), (6,w)]. Find the following: 1. R. 2. R 3. R-1 4. R-1 6. (R.1)- 1I. Let the universal set U - {1, 2, 3, . .., 10} . Let A = {1, 4, 7, 10}, B = {1, 2, 3, 4, 5 }, and C = {2, 4, 6, 8}. List the elements of each set and draw its corresponding venn diagram. 1. U' 2. Bno 3. BOU 4. B'n (C - A) 5. A'nB'UC 2. 100 students were interviewed. 28 took PE, 31 took BIO, 42 took ENG, 9 took PE and BIO, 10 took PE and ENG, 6 took BIO and ENG, 4 took all three subjects. a) How many students took none of the three subjects? b) How many students took PE but not BIO or ENG? c) How many students took BIO and PE but not ENG? d) How many students took exactly 2 of 3 subjects? e) How many students took any 2 of 3 subjects? f) How many students took any of the 3 subjects? g) How many students took none of the 3 subjects?1. Determine which of the following functions are Injective, Surjective or both Injective and Surjective (Injective). 1. f : N-Z - {0} defined by f(n) = -n for all n EN. 2. f : Z-Z defined by f(x) = 4x-+3 for all x EZ . 3. f : R-R defined by f (x) = x for all x E R . 4. f : R-R defined by f (x) = 3- for all x ER. II. Find the inverse of the given function. State the domain and range of f and f -1. 2 1. f(x) =5-,X 2. f(x) =6-5x2 3. f(x) = -8x+24 3 4. f(x) =x+11 5. f (x ) = 4x2 +7Ill. Define the of the following permutations given the following functions. Let A = {1, 2, 3, 4, 5} 1 = (3 7 3 2 4) 14- (3 2 3 5 4) f2 = (3 4 2 5 3) F5 - (8 2 3 4 5) 1 3 = (4 3 1 3 2) 16 - (34 3 34) 1. f6 of3 2. (f6) -of2 3. f5 0 (f 4) -1 4. (f4 -1 . ( f2 ) - 1 ) - 1 5 . ( (f1 ) - 1 0 (5 )