Show that the following four conditions are equivalent : (i) `A sub B` (ii) `A -B = phi` (iii)`A uu B = B` (iv) `A nn B = A`

Prove that : (i) A sub (A uu B) (ii) B sub (A uu B) .

Prove that : (i) (A nn B) sub A (ii) (A nn B) sub B .

Prove the following : A sub B iff A nn B=A .

Prove the following : A sub B iff A uu B=B .

If A = A uu B , prove that B = A nn B .

Given the following informations about the non-zero vectors A, B and C (i)(AtimesB)timesA=0 : (ii)B*B=4 (iii) A*B=-6 : (iv)B*C=6 which one of the following holds good?

Prove the following : B sub A implies A uu B=A .

Prove that A uu B= A nn B implies A=B.

Shade the following : A^(c) nn (B uu C) in the given Venn diagram.

Prove the following : A-B=A-(A nn B) .