Question

pls answer in english​

Answer 1

Answer:

Step-by-step explanation:

Given that,

A = {x∈ N / 1 < x < 4 } ,B ={ x ∈W / 0 < x < 2} and C = { x ∈N / x < 3 }

A = { 2, 3 } , B = { 1 } and C = { 1, 2}

L.H.S. = A × ( B ∩ C )

( B ∩ C ) = { 1 } ∩ { 1, 2 } = { 1 }

∴ A × ( B ∩C ) = { 2, 3 } × { 1 } = { ( 2,1 ), ( 3,1 ) }

R.H.S. = ( A × B ) ∩ ( A × C )

( A × B ) = { 2, 3 } × { 1 } = { ( 2,1 ) , ( 3,1 ) }

( A × C ) = { 2,3 } × { 1, 2 } = { ( 2,1 ) , ( 2,3 ) , ( 3, 1 ) , ( 3,2 ) }

∴ ( A × B ) ∩ ( A × C ) = { ( 2,1 ), ( 3,1 ) } ∩ { ( 2,1 ), ( 2,3 ), ( 3,1 ), ( 3,2 ) } = { ( 2,1 ), ( 3, 1 ) }

LL.H.S . = R.H.S.

Hence,it is verified.