Solution to A. SET. Let A, B and C are sets and U be universal set. U … - Sikademy
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Archangel Macsika

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. 𝐡 βˆͺ 𝐢 2. 𝐴 βˆ’ 𝐡 π‘₯ 𝐢 3. π‘ƒπ‘œπ‘€π‘’π‘Ÿ 𝑠𝑒𝑑 π‘œπ‘“ 𝐢 4. |𝑃(𝐡)| B. SEQUENCES. Consider the sequence {Sn} defined by Sn = 2n – 5, where 𝒏 β‰₯ βˆ’πŸ. Find for: 1. βˆ‘π‘†π‘–1𝑖=βˆ’1 2. βˆπ‘†π‘–4𝑖=2 C. RELATION. Consider X = {-3, -2, -1, 0, 1} defined by (x,y) ∈ 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)

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1 Β B\cupΒ C={0,2,4,6,b,c,d}

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

3.Power set of C={\phiΒ ,{b},{c},{d},{b,c},{b,d},{c,d},{b,c,d}}


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


Relation R is defined as-


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.

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Question ID: mtid-5-stid-8-sqid-3137-qpid-1836