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

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

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

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

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

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)

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

Prove that A uuB=A nn B if A=B .

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

Observe the venn diagram b)Verify that (A-B) uu (A nn B)=A

If A+B+C=pi . Then prove that cosA=-cos(B+C)