If A = {x:x is a prime number and x < 20} B = {x : x = 2x + 1, x ∈ W

1.	If A = {x:x is a prime number and x < 20} B = {x : x = 2x + 1, x ∈ W and x < 9), find i) A ∩ B ii) B ∩ A iii) A – B iv) B – A What do you observe ?
Answer» A = {2, 3, 5, 7, 11, 13, 17, 19} B = {1, 3, 5, 7} i) A ∩ B = {2, 3, 5, 7,11, 13,17,19} ∩ {1,3, 5,7} = {3,5,7} . ii) B ∩ A = {1, 3, 5, 7} ∩ {2, 3, 5, 7, 11, 13, 17, 19} = {3,5,7} iii) A – B = {2, 3,5,7, 11, 13, 17, 19} – {1,3, 5,7} = {2, 11, 13, 17, 19} iv) B – A = {1,3,5, 7} – {2, 3, 5, 7, li; 13, 17, 19}= {1} ∴ We observed A ∩ B = B ∩ A A – B ≠ B – A

If A = {x:x is a prime number and x < 20} B = {x : x = 2x + 1, x ∈ W and x < 9), find i) A ∩ B ii) B ∩ A iii) A – B iv) B – A What do you observe ?

Answer»

A = {2, 3, 5, 7, 11, 13, 17, 19}

B = {1, 3, 5, 7}

i) A ∩ B = {2, 3, 5, 7,11, 13,17,19} ∩ {1,3, 5,7} = {3,5,7} .

ii) B ∩ A = {1, 3, 5, 7} ∩ {2, 3, 5, 7, 11, 13, 17, 19} = {3,5,7}

iii) A – B = {2, 3,5,7, 11, 13, 17, 19} – {1,3, 5,7} = {2, 11, 13, 17, 19}

iv) B – A = {1,3,5, 7} – {2, 3, 5, 7, li; 13, 17, 19}= {1}

∴ We observed A ∩ B = B ∩ A

A – B ≠ B – A