Let P = {a, b, c}, Q = {g, h, x, y} and R = {a, e, f, s}. Find the following:

(i) P R

(ii) Q + R

(iii) R (P + Q)

(i) The set which will be obtained from P R is called as a complement set. It indicates the elements which are only a part of the set P and doesn’t belong to R.

Mathematically,

P R = {x|x ∈ p but x ∉ R}

We are given

P = {a, b, c},

R = {a, e, f, s}

So using the given values

P R = {a, b, c} {a, e, f, s}

= {b, c}

(ii) The above statement can also be written as (Q Ո R). An intersection operation between two sets gives a set which contain the elements which are common to both the sets.

We are given

Q = {g, h, x, y}

R = {a, e, f, s}

So using the value given

(Q Ո R) = {g, h, x, y} Ո {a, e, f, s}

= Ø

It’s called as a disjoint set as both the sets Q and R doesn’t have any elements in common.

(iii) Before proceeding we will split the entire operation into two halves. We know that the statement (P + Q) can be written as (P Ո Q) and it will give a set of all common elements

We are given that

P = {a, b, c},

Q = {g, h, x, y}

R = {a, e, f, s}

So using the values given

(P Ո Q) = {a, b, c} Ո {g, h, x, y}

= Ø [disjoint sets as there are no common elements]

Now the statement R (P + Q) shows a difference operation of two sets. The difference operation will give elements which are a part of set R only and doesn’t exist in (P ⋂ Q).

So using the values given

R (P + Q) = R (P⋂ Q)

= {a, e, f, s} Ø

= {a, e, f, s} (.ans)