Let `A={varphi{varphi},1,{1,varphi},2}dot` Which of the following are true? `varphi A` ii. `2subA` iii. `{2,{1}} A`

Let A={varphi{varphi},1,{1,varphi},2} .Which of the following are true? varphi A ii.2sub A iii.{2,{1}}A

Let A={varphi{varphi},1,{1,varphi},2}. Which of the following are true? {1}A ii.{{varphi}}sup A iii.{2,varphi}sub A

Let A={varphi{varphi},1,{1,varphi},2}. Which of the following are true? {{2},{1}}A ii.{varphi,{varphi},{1,varphi}}sub A

Let A= {1,2,{3,4},5}. Which of the following statements are correct and why ? (i) {3,4}subA (ii) {3,4}inA (iii) {{3,4}}subA (iv) 1inA (v) 1subA (vi) {1,2}subA . (vii) {1,2,5}inA (viii) {1,2,3}subA . (ix) phiinA (x) phisubA (xi) {phi}subA .

Let A={{1,2,3},{4,5},{6,7,8}} Determine which of the following is true or false: {{4,5}}sub A varphi A varphi sub A

Write down all possible subset of each of the following set: {varphi}

Let A={a,b,{c,d},e}. Which of the following statements are false and why? {a,b,e}in A{a,b,c}sub A varphi A{varphi}sub A

Prove that the product of matrices [cos^(2)theta cos theta sin theta cos theta sin theta s in^(2)theta] and [cos^(2)varphi cos varphi sin varphi cos varphi sin varphi s in^(2)varphi] is the null matrix,when theta and varphi differ by an odd multiple of (pi)/(2) .