**A. SET. Let A, B and C are sets and U be universal set. U = {-1, 0, 1, 2, 3, 4, 5, 6, a, b, c, d, e} A = {-1, 1, 2, 4} B = {0, 2, 4, 6} C = {b, c, d} Find for the following. Show complete solutions. (3 pts each) 1. π΅ βͺ πΆ 2. π΄ β π΅ π₯ πΆ 3. πππ€ππ π ππ‘ ππ πΆ 4. |π(π΅)| B. SEQUENCES. Consider the sequence {Sn} defined by Sn = 2n β 5, where π β₯ βπ. Find for: 1. βππ1π=β1 2. βππ4π=2 C. RELATION. Consider X = {-3, -2, -1, 0, 1} defined by (x,y) β R if x β₯ y. Find for: 1. Elements of R (3 pts) 2. Domain and Range of R (2 pts) 3. Draw the digraph (3 pts) 4. Identify the properties of R (2pts)**

The **Answer to the Question**

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**Here's the Solution to this Question**

A.

1 Β B$\cup$Β C={0,2,4,6,b,c,d}

2.$A-B \times C$Β ={-1,1} x {b,c,d}={(-1,b),(-1,c),(-1,d),(1,b),(1,c),(1,d)}

3.Power set of C={$\phi$Β ,{b},{c},{d},{b,c},{b,d},{c,d},{b,c,d}}

4.$|P(B)|=2^4=16$

B. 1.$\sum_{i=-1}^{i=1}S_i=\sum _{i=-1}^{i=1}2i+5=2(-1)+5+2(0)+5+2(1)+5=15$

2.$\sum_{i=2}^{i=4}S_i=\sum _{i=2}^{i=4}(2i+5)=2(2)+5+2(3)+5+2(4)+5=4+6+8+15=33$

C.X={-3,-2,-1,0,1}

Relation R is defined as-

R={(-2,-3),(-1,-3),(-1,-2),(0,-3),(0,-2),(0,-1),(1,-3),(1,-2),(1,-1),(1,0)}

1.Elements of R are (-2,-3),(-1,-3),(-1,-2),(0,-3),(0,-2),(0,-1),(1,-3),(1,-2),(1,-1),(1,0)

2.Domain of R={-2,-1,0,1}

Range of R ={-3,-2,-1,0}

3.Diagraph is-

4.Properties of R-

(i) R is the subset of the cartesian product form from the given set.

(ii) R can be reflexive,transitive and symmetric in nature.