Using properties of sets, show that
`A ∩ ( A ∪ B ) = A`.

By using properties of determinants , show that : {:|( 1,x,x^(2) ),( x^(2) ,1,x) ,( x,x^(2), 1) |:} =( 1-x^(3)) ^(2)

IF a+b+c ne 0 and {:|(a,b,c),(b,c,a),(c,a,b)| =0, then using properties of determinants, prove that a=b=c

Using properties of determinants prove that : |(1+a,1,1),( 1,1+b,1),(1,1,1+c)| =abc +bc +ca +ab

For any sets A and B, show that P ( A ∩ B ) = P ( A ) ∩ P ( B ) .

Let A, B, and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C . Show that B = C .

Using determinants show that points A (a, b+ c) , B (b,c+ a) and C ( c, a+ b) are collinear.

Using determinants show that points A(a, b + c), B(b, c + a) and C(c, a + b) are collinear.

Using the property of determinants prove that {:|( 3a,-a+b,-a+c),( -b+a, 3b,-b+c) ,( -c+a,-c+b,3c) |:} = 3( a+b+c) ( ab+bc+ca)

Show that for any sets A and B, A = ( A ∩ B ) ∪ ( A – B ) and A ∪ ( B – A ) = ( A ∪ B )

Using the Properties of determinants, prove the following: {:|(1,1,1),(a,b,c),(bc,ca,ab)|=(a-b)(b-c)(c-a)