Question

here are the meanings of some of the symbols that appear in the statements below.

• ⊆ means \is a subset of.\
• ⊂ means \is a proper subset of.\
• ⊈ means \is not a subset of.\
• ∅ is the empty set.

for each statement, decide if it is true or false.
(a) {t, w}⊂∅
true false
(b) {1, 2, 3, 4}⊈{2, 3}
true false
(c) {12, 15, 16, 17}⊆{12, 15, 16, 17}
true false
(d) {c, f, j}⊂{c, d, f, g, h, j}
true false

Explanation:

Step1: Analyze statement (a)

A non - empty set cannot be a proper subset of the empty set. The empty set has no elements, while $\{t, w\}$ has elements. So $\{t, w\}\subset\varnothing$ is false.

Step2: Analyze statement (b)

The set $\{1,2,3,4\}$ has elements $1$ and $4$ which are not in $\{2,3\}$. So $\{1,2,3,4\}
ot\subseteq\{2,3\}$ is true.

Step3: Analyze statement (c)

Every set is a subset of itself. So $\{12,15,16,17\}\subseteq\{12,15,16,17\}$ is true.

Step4: Analyze statement (d)

The set $\{c,f,j\}$ has elements that are all in $\{c,d,f,g,h,j\}$, and $\{c,d,f,g,h,j\}$ has additional elements. So $\{c,f,j\}\subset\{c,d,f,g,h,j\}$ is true.

Answer:

(a) False
(b) True
(c) True
(d) True