1.Set TheoryMedium

Match each of the set on the left in the roster form with the same set on the right described in set-builder form:

$(i)$ $\{1,2,3,6\}$ $(a)$ $\{ x:x$ is a prime number and a divisor $6\} $

$(ii)$ $\{2,3\}$ $(b)$ $\{ x:x$ is an odd natural number less than $10\} $

$(iii)$ $\{ M , A , T , H , E , I , C , S \}$ $(c)$ $\{ x:x$ is natural number and divisor of $6\} $

$(iv)$ $\{1,3,5,7,9\}$ $(d)$ $\{ x:x$ a letter of the work $\mathrm{MATHEMATICS}\} $

Solution

$(i)$ All the elements of this set are natural numbers as well as the divisors of $6 .$ Therefore, $(i)$ matches with $(c).$

$(ii)$ It can be seen that $2$ and $3$ are prime numbers. They are also the divisors of $6 .$ Therefore, $(ii)$ matches with $(a).$

$(iii)$ All the elements of this set are letters of the word $MATHEMATICS.$ Therefore, $(iii)$ matches with $(d).$

$(iv)$ All the elements of this set are odd natural numbers less than $10 .$ Therefore, $(iv)$ matches with $(b).$

Let $A, B,$ and $C$ be the sets such that $A \cup B=A \cup C$ and $A \cap B=A \cap C$. Show that $B = C$

Medium

Easy

Easy

Easy

Easy

$(i)$ $\{1,2,3,6\}$	$(a)$ $\{ x:x$ is a prime number and a divisor $6\} $
$(ii)$ $\{2,3\}$	$(b)$ $\{ x:x$ is an odd natural number less than $10\} $
$(iii)$ $\{ M , A , T , H , E , I , C , S \}$	$(c)$ $\{ x:x$ is natural number and divisor of $6\} $
$(iv)$ $\{1,3,5,7,9\}$	$(d)$ $\{ x:x$ a letter of the work $\mathrm{MATHEMATICS}\} $