Which of the following is a true statement?

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Question

(A) In set theory, the symbol $\subseteq$ denotes a subset relationship, while $\in$ denotes an element relationship.
For the set $A = \{a, b, c\}$:

Vedclass · Accepted Answer

${a} \subseteq {a,b,c}$

Vedclass · Answer

(A) In set theory, the symbol $\subseteq$ denotes a subset relationship, while $\in$ denotes an element relationship.
For the set $A = \{a, b, c\}$:
$1$. The set ${a}$ is a subset of $A$ because every element of ${a}$ is also an element of $A$. Thus, ${a} \subseteq {a, b, c}$ is a true statement.
$2$. The set ${a}$ is not an element of $A$; only $a$ is an element of $A$. Thus, ${a} \in {a, b, c}$ is false.
$3$. The empty set $\phi$ is a subset of every set, but it is not an element of $A$ unless explicitly stated. Thus, $\phi \in {a, b, c}$ is false.
Therefore, the correct statement is ${a} \subseteq {a, b, c}$.

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