Decide which sets are proper subset of other.

 Decide which sets are proper subset of other.

(i) T = {t/t is a rectangle}

(ii) P = {p/p is a parallelogram}

(iii) S = {s/s is a square}

(iv) X = {x/x is a quadrilateral}

Solution:

    T = {t/t is a rectangle}

Since rectangle is also a quadrilateral therefore T is proper subset of X.

    or    T⊂X

P = {p/p is a parallelogram}

Since parallelogram is also a quadrilateral therefore P is proper subset of X.

or     P⊂X.

S = {s/s is a square}

Since square is also a quadrilateral therefore S is proper subset of X.

or    S⊂X

Now each of T,F,S is a proper subset of X therefore 

    S⊂T, S⊂P, T⊂P