Question

ple 30 Show that A U B = An B implies A = B​

Answer 1

Solution :

let a € A

then A € A ∪ B

since A ∪ B = A ∩ B ,

then, a € A ∩ B

so, a € B therefore A ⊂ B

Similarly if b € B Then b € A ∪ B

since

A ∪ B = A ∩ B , b € A ∩ B

so,

b € A

therefore

B ⊂ A , thus A = B

Extra information :

C = {1, 2, 3, 4} and D = {3, 4, 5}

Symbol ⠀⠀⠀⠀⠀⠀⠀ Example

A ∪ B ⠀⠀⠀⠀⠀⠀⠀⠀C ∪ D = {1, 2, 3, 4, 5}

A ∩ B ⠀⠀⠀⠀⠀⠀⠀⠀C ∩ D = {3, 4}

A ⊆ B ⠀⠀⠀⠀⠀⠀⠀⠀{3, 4, 5} ⊆ D