PROBLEM SOLVING. 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. 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. β1π=β1 ππ (5 pts) 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 2. Domain and Range of R 3. Draw the digraph 4. Identify the properties of R
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Solution:
(A):
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}
1. π΅ βͺ πΆ = {0, 2, 4, 6, b, c, d}
2.Β
Now,Β
3. πππ€ππ π ππ‘ ππ πΆ
4. |π(π΅)|Β , where n is the number of elements in set B.
(B):
(C):
Consider X = {-3, -2, -1, 0, 1} defined by (x,y)Β βΒ R if xΒ β₯Β y.
1.
2. Domain of R
And range of R
3. Digraph of R:
4.
Reflexive:
It is clearly reflexive asΒ
Symmetric:
It is clearly not symmetric asΒ Β butΒ Β is not true,Β
Moreover,Β Β butΒ
Transitive:
Β which is trueΒ
Hence, it is transitive.