Use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements.
If 𝑃 ⊆ 𝑄, then 𝑃 ⊆ 𝑅.
If 𝑃 ⊆ 𝑅, then 𝑃 ⊆ 𝑆.

The correct answer is: Hence, the new conditional statement is “If 𝑃 ⊆ 𝑄, then 𝑃 ⊆ 𝑆”.

It is given that: If 𝑃 ⊆ 𝑄, then 𝑃 ⊆ 𝑅 and If 𝑃 ⊆ 𝑅, then 𝑃 ⊆ 𝑆. So if we take
p = 𝑃 ⊆ 𝑄
q = 𝑃 ⊆ 𝑅
r = 𝑃 ⊆ 𝑆
So can write the given statement “If 𝑃 ⊆ 𝑄, then 𝑃 ⊆ 𝑅” as p  q and the statement “ If 𝑃 ⊆ 𝑅,
then 𝑃 ⊆ 𝑆” can be written as q  r.
So, we can conclude that p  r which means that If 𝑃 ⊆ 𝑄, then 𝑃 ⊆ 𝑆.
Final Answer:
Hence, the new conditional statement is “If 𝑃 ⊆ 𝑄, then 𝑃 ⊆ 𝑆”.