Using properties of sets,prove that
`(A uu B)-C=(A-C) uu (B-C)`.

Using the properties of sets,prove that A-(B-C)=(A-B) uu (A nn C)

Using properties of sets, show that i) 'A ⋃(A ⋂ B)=A' ii) 'A ⋂(A ⋃ B)=A'

Using properties 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)

By using properties of determinants, prove that |[0,a ,-b],[-a,0,-c],[b,c,0]|=0

By using properties of determinants, prove that |[-a^2,ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^2

Using properties of determinants prove the following. abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

By using the properties of determinants,prove that |[a^2+1,ab ,ac],[ab,b^2+1,bc],[ca ,cb,c^2+1]|=1+a^2+b^2+c^2

using properties of determinants, prove that abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a) .

Using properties of determinants prove the following. abs[[b+c,a,a],[b,c+a,b],[c,c,a+b]]=4abc

Using properties of determinants prove the following. abs[[1,a,bc],[1,b,ca],[1,c,ab]]=(a-b)(b-c)(c-a)