Prove analytically that `A-B=AcapB^c`

Prove analytically that (A-B)cupB=AcupB

Prove analytically that (A-B)cup(B-A)=(AcupB)-(AcapB)

Show analytically how stationary wave are they formed due to superposition of two waves.

Mention one analytical application of co-ordination compound.

Prove that sin(A-B)/(cosAcosB)+sin(B-C)/(cosBcosC)+sin(C-A)/(cosCcosA)=0

By constructing truth table, prove the following pairs of compound statement have identical truth value. A^^B(B vv C) and (A ^^ B) vv (A ^^ C)

A,B,C are any three sets. Applying various laws prove that : (A-C) nn (B-C)=(A nn B)-C

For any three sets A,B,C prove that : A-(B uu C ) = (A-B) nn (A-C)

A,B,C are any three sets. Applying various laws prove that : A-(B nn C) = (A-B) uu (A-C)

Prove that (b+c-a)^3+(c+a-b)^3+(a+b-c)^3-(a+b+c)^3+108abc = 84abc