Question

Given that S = { a, b, c, d , e } and T = { a, c, e }, then one of these is untrue (a) T is a subset of S (b) T⊆S (c) S≠T (d) S⊆T
A = {x / x is an odd number between 5 and 21} is same as------------ (a) A = {5,7,9,11,13,15,17,19} (b) A = {5,7,9,11,13,15,17,19,21} (c) A = {x : x is an odd number between 5 and 21} (d) A = {7,9,11,13,15,17,19,21}

Answer 1

ANSWER ON QUESTION #54796 – Math – Set Theory

1. Given that $S = \{ a, b, c, d, e \}$ and $T = \{ a, c, e \}$, then one of these is untrue

(a) T is a subset of S

(b) $T \subseteq S$

(c) $S \neq T$

(d) $S \subseteq T$

Solution: (d) is untrue, because, for example, the element $d \in S$, but $d \notin T$

2. $A = \{ x / x \text{ is an odd number between 5 and 21} \}$ is same as

(a) $A = \{5,7,9,11,13,15,17,19\}$

(b) $A = \{5,7,9,11,13,15,17,19,21\}$

(c) $A = \{ x : x \text{ is an odd number between 5 and 21} \}$

(d) $A = \{7,9,11,13,15,17,19,21\}$

Solution: (a) and (d) are untrue.

In case (a) the number 21 is not belong to the set $A = \{5,7,9,11,13,15,17,19\}$.

In case (d) the number 5 is not belong to the set $A = \{7,9,11,13,15,17,19,21\}$, but 5 is an odd number between 5 and 21.

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