Maths-

General

Easy

Question

# 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.

Hint:

### Law of Syllogism states that:

1) if p q is true

2) If q r is true

then we can conclude that p r is also true.

## 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”.

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