. a) If A={x:x is factor of 12) B ={x:x is prime factor of 12) then find
(i) A-B
(ii) B-A
(iii) Is A-B-B-AP
Answers
Given : A={x:x is factor of 12} B={x:x is prime factor of 12}
To Find : 1.) A - B
2.) B - A
3.) Is A - B = B - A?
Solution:
A={x:x is factor of 12}
12 = 1 * 12
12 = 2 * 6
12 = 3 * 4
A = { 1 , 2 , 3 , 4 , 6 , 12 }
B={x:x is prime factor of 12}
2 & 3 are prime numbers
Hence
B= { 2 , 3}
A - B = x ∈ A but x ∉ B
A - B = A - A ∩ B
A ∩ B = { 2 , 3}
A - B = { 1 , 2 , 3 , 4 , 6 , 12 } - { 2 , 3}
=> A - B = { 1 , 4 , 6 , 12 }
B - A = x ∈ B but x ∉ A
B - A = B - A ∩ B
=> B - A = { 2 , 3} - { 2 , 3}
=> B - A = { } or Ф
A - B = { 1 , 4 , 6 , 12 }
B - A = { } or Ф
A - B ≠ B - A
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