Question

here are the meanings of some of the symbols that appear in the statements below. - $\subseteq$ means \is a subset of.\ - $\subset$ means \is a proper subset of.\ - $\
subseteq$ means \is not a subset of.\ - $\varnothing$ is the empty set. for each statement, decide if it is true or false. (a) $\varnothing \
subseteq \\{q, s, t, u\\}$ \bigcirc true \bigcirc false (b) $\\{1, 2, 3, 4, 5, 6\\} \
subseteq \\{1, 4, 6\\}$ \bigcirc true \bigcirc false (c) $\\{d, g, j\\} \subset \\{c, d, f, g, h, j\\}$ \bigcirc true \bigcirc false (d) $\\{13, 14, 19\\} \subseteq \\{13, 14, 19\\}$ \bigcirc true \bigcirc false

Explanation:

Part (a)

Step1: Recall empty set subset rule

The empty set \(\varnothing\) is a subset of every set. So \(\varnothing\subseteq \{q, s, t, u\}\), which means \(\varnothing
subseteq \{q, s, t, u\}\) is false.

Step1: Check subset condition

A set \(A\) is a subset of \(B\) if every element of \(A\) is in \(B\). For \(A = \{1, 2, 3, 4, 5, 6\}\) and \(B=\{1, 4, 6\}\), elements \(2, 3, 5\) of \(A\) are not in \(B\). So \(A
subseteq B\) is true.

Step1: Check proper subset condition

A proper subset \(A\subset B\) means \(A\subseteq B\) and \(A
eq B\). For \(A = \{d, g, j\}\) and \(B = \{c, d, f, g, h, j\}\), every element of \(A\) is in \(B\) and \(A
eq B\), so \(A\subset B\) is true.

Answer:

False

Part (b)