# Lecture - 3 Chapter 1 Sets

“Nobody ever wrote down a plan to be broke, fat, lazy. or stupid. Those things are what happen when you don’t have a plan.” – Larry Winget

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 NCERT EXERCISE 1.4
1. Find the union of each of the following pairs of sets:
• (i) X = {1, 3, 5} Y = {1, 2, 3}
• A = { a, e, i, o, u} B = {a, b, c}
• A = {x : x is a natural number and multiple of 3}
B = {x : x is a natural number less than 6}
• A = {x : x is a natural number and 1 < x ≤ 6 }
B = {x : x is a natural number and 6 < x < 10 }
• (v) A = {1, 2, 3}, B = f
1. Let A = { a, b }, B = {a, b, c}. Is A ⊂ B ? What is A ∪ B ?
1. If A and B are two sets such that A ⊂ B, then what is A ∪ B ?
1. If A = {1, 2, 3, 4},B = {3, 4, 5, 6}, C = {5, 6, 7, 8 }and D = { 7, 8, 9, 10 }; find
• (i) A ∪ B
• A ∪ C
• B ∪ C
• B ∪ D
• (v) A ∪ B ∪ C
• A ∪ B ∪ D
• B ∪ C ∪ D
1. Find the intersection of each pair of sets of question 1 above.
1. If A = { 3, 5, 7, 9, 11 },B = {7, 9, 11, 13},C = {11, 13, 15} and D = {15, 17}; find
• (i) A ∩ B
• B ∩ C
• A ∩ C ∩ D
• A ∩ C
• (v) B ∩ D
• A ∩ (B ∪ C)
• A ∩ D
• A ∩ (B ∪ D)
• ( A ∩ B ) ∩ ( B ∪ C )
• (x) ( A ∪ D) ∩ ( B ∪ C)
##### Clip - 1
1. If A = {x : x is a natural number},B = {x : x is an even natural number}C = {x : x is an odd natural number} and D = {x : x is a prime number }, find
• (i) A ∩ B
• A ∩ C
• A ∩ D
• B ∩ C
• (v) B ∩ D
• C ∩ D
1. Which of the following pairs of sets are disjoint
• (i) {1, 2, 3, 4} and {x : x is a natural number and 4 ≤ x ≤ 6 }
• { a, e, i, o, u } and { c, d, e, f }
• {x : x is an even integer } and {x : x is an odd integer}
1. If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 },C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }; find
• (i) A – B
• A – C
• A – D
• B – A
• (v) C – A
• D – A
B – C
• B – D
• C – B
• (x) D – B
• C – D
• D – C
1. If X= { a, b, c, d } and Y = { f, b, d, g}, find
• (i) X – Y
• Y – X
• X ∩ Y
1. If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q?
1. State whether each of the following statement is true or false. Justify your answer.
• (i) { 2, 3, 4, 5 } and { 3, 6} are disjoint sets.
• {a, e, i, o, u} and {a, b, c, d} are disjoint sets.
• {2, 6, 10, 14} & {3, 7, 11, 15} are disjoint sets.
• { 2, 6, 10 } and { 3, 7, 11} are disjoint sets.