Fsc Part 1 Mathematics (Complete Solution)

# Q10 Which pairs of sets are equivalent? which of them are also equal?

(i) {a,b,c},{1,2,3}

Ans: This Pairs of set is equivalent but are not equal because the set {a,b,c} and {1,2,3} have same number of elements.

(ii) The set of the first 10 whole members,{0,1,2,3,...,9}

Ans:The Ser of the first 10 whole numbers is {0,1,2,3,4,5,6,7,8,9} which is same and identical to second given set ,so it is equivalent and equal.

(iii) Set of angles of a quadrilateral ABCD,

Ans:There are four angles and four sides in a quadrilateral ABCD,so the set of  angles of a  quadrilateral ABCD is equivalent to the set of the sides of the same quadrilateral.So they are equivalent but angles and sides are different things so they are not equal.

(iv) Set of the sides of a hexagon ABCDEF,

set of the angles of the same hexagon;

Ans:There are six sides and six angles in hexagon ABCDEF so they are equivalent but angles and sides are different things so they are not equal.

(Hexagon)

(v) {1,2,3,4,...},{2,4,6,8,....}

Ans: Sine there exist 1 to 1 correspondence between the set of natural numbers and the set of positive even integers so these are equivalent but not equal.

(vi) {1,2,3,4,..},{1,1/2,1/3,1/4,...}

Ans:Sine there exist 1 to 1 correspondence between the elements of the sets, so these are equivalent but are not equal.

(vii) {5,10,15,20,.....,55555},{5,10,15,20,...}

Ans: Since {5,10,15,20,.....,55555},{5,10,15,20,...} is finite set while {5,10,15,20,...} has finite set so these are neither equivalent nor equal.