Match each of the set on the left described in the roster form with the same set on the right described in the set-builder form:
$(i) \{ P,R,I,N,C,A,L\} $ $(a) \{ x:x \text{ is a positive integer and is a divisor of } 18\} $ $(ii) \{ 0\} $ $(b) \{ x:x \text{ is an integer and } x^2 - 9 = 0\} $ $(iii) \{ 1,2,3,6,9,18\} $ $(c) \{ x:x \text{ is an integer and } x + 1 = 1\} $ $(iv) \{ 3, -3\} $ $(d) \{ x:x \text{ is a letter of the word } PRINCIPAL\} $
| $(i) \{ P,R,I,N,C,A,L\} $ | $(a) \{ x:x \text{ is a positive integer and is a divisor of } 18\} $ |
| $(ii) \{ 0\} $ | $(b) \{ x:x \text{ is an integer and } x^2 - 9 = 0\} $ |
| $(iii) \{ 1,2,3,6,9,18\} $ | $(c) \{ x:x \text{ is an integer and } x + 1 = 1\} $ |
| $(iv) \{ 3, -3\} $ | $(d) \{ x:x \text{ is a letter of the word } PRINCIPAL\} $ |
(A) In $(d)$,the word $PRINCIPAL$ consists of the letters $P, R, I, N, C, A, L$ (since $P$ and $I$ are repeated,they are written once in the set). Thus,$(i)$ matches $(d)$.
In $(c)$,$x + 1 = 1$ implies $x = 0$. Thus,$(ii)$ matches $(c)$.
In $(a)$,the positive divisors of $18$ are $1, 2, 3, 6, 9, 18$. Thus,$(iii)$ matches $(a)$.
In $(b)$,$x^2 - 9 = 0$ implies $x^2 = 9$,so $x = 3$ or $x = -3$. Thus,$(iv)$ matches $(b)$.
The correct matching is $(i)-(d), (ii)-(c), (iii)-(a), (iv)-(b)$.
In $(c)$,$x + 1 = 1$ implies $x = 0$. Thus,$(ii)$ matches $(c)$.
In $(a)$,the positive divisors of $18$ are $1, 2, 3, 6, 9, 18$. Thus,$(iii)$ matches $(a)$.
In $(b)$,$x^2 - 9 = 0$ implies $x^2 = 9$,so $x = 3$ or $x = -3$. Thus,$(iv)$ matches $(b)$.
The correct matching is $(i)-(d), (ii)-(c), (iii)-(a), (iv)-(b)$.
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