Page 16 - 7-Math-1 SETS

1.1S. eQtsuadratic Equations eeLLeeaarrnn..PPuunnjjaabb

(i) A ∩ B = B ∩ A (ii) A U B = B U A (iii) B U C = C U B
(iv) B ∩ C = C ∩ B (v) A ∩ C = C ∩ A (vi) A U C = C U A
2. If X = {1, 3, 7}, Y= {2, 3, 5} and Z = {1, 4, 8}, then verify that:
(i) X ∩ (Y ∩ Z) = (X ∩ Y) ∩ Z (ii) X U (Y U Z) = (X U Y) U Z
3. If S = {–2, –1, 0, 1}, T= {–4, –1, 1, 3} and U= {0, ±1, ±2}, then verify
that:
(i) S ∩ (T ∩ U) = (S ∩ T) ∩ U (ii) S u (T j U) = (S j T) j U
4. If O = {1, 3, 5, 7.....}, E = {2, 4, 6, 8......} and N = {1, 2, 3, 4....}, then
verify that:
(i) O ∩ (E ∩ N) = (O ∩ E) ∩ N (ii) O j (E j N) = (O j E) j N
5. If U = {a, b, c, ....,z}, S = {a, e, i, o, u} and T = {x, y, z}, then verify that:
(i) S U f = S (ii) T ∩ U = T (iii) S ∩ S’ = f (iv) T U T’ = U
6. If A = {1, 7, 9, 11}, B = {1, 5, 9, 13}, and C = {2, 6, 9, 11}, then verify
that:
(i) A - B ≠B - A (ii) A - C ≠C - A
7. If U = {0, 1, 2,....,15}, L = {5, 7, 9,....,15}, and M = {6, 8, 10, 12, 14},
then verify the identity properties with respect to union and
intersection of sets.

1.3 Venn Diagram

A Venn diagram is simple closed figures to show sets and
the relationships between different sets.

Venn diagram were introduced by a British
logician and philosopher “John Venn” (1834
- 1923). John himself did not use the term
“Venn diagram” Another logician “Lewis”
used it first time in book “A survey of symbolic
logic”

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