Question

Esamine whether the following statements are true or false :
` (i) {a,b} cancel(sub) {b,c} (ii) {a} in {a,b,c}
(iii) ` {phi} sub {a, b, c } `
(iv) `{a,e} sub {x:x " is a vowel in the English alphabet "}`
` (v) {x:x in W, x+5 =5}=phi`
`(vi) a in {{a} , b}`
`(vii) `{a} sub {{a},b}`
` (viii) {b,c} sub {a, c}}`
`(ix) {a,a,b,b}={a,b}`
(x) {a,b,a, b,a,b...}` " is an infinte set".
(xi) If `A=` set of all circles of unit radius in a plane and B= set of all circles in the same plane then ` A sub B`.

Answer 1

Correct Answer - (i) False
(ii) False
(iii) False
(iv) True
(v) False
(vi) False
(vii) False
(viii) False
(ix) True
(x) False
(xi) True.
(ii) `a in {a,b,c}` is true, So, ` {a}, in { a,b,c}` is a false.
(iii) `phi sub {a,b,c} " is true and " {phi} sub { a,b,c}` is false.
(iv) `{a, e} sub {a, e, i,o,u}` is true.
(v) ` {x:x in W, x + 5=5}={0}`.
(vi) `{{a} , b }` has two elements , namely `{a}` and b.
(vii) `{a} in {{ a} , b}`. So `{a}, sub {{a} , b}` is false.
(viii) ` {b,c} in {a, {b, c}}`. So , ` {b, c } sub {a,{b,c}}` is false
(ix) Repetition of elements in a set has no meaning.
(x) Given set ` = {a,b}`, which is finite.