I need help on converting these to the correct logical notation form using only the propositional connectives and the quantifiers. I'd appreciate if there are some explanation for the reasons of converting in such ways.(adsbygoogle = window.adsbygoogle || []).push({});

This is what I got so far:

(a) Problem: A ⊆ B ∩ C

What I tried getting:∀x(x ∈ A → x ∈ B ∧ x ∈ C)

(b) Problem: A ⊆ {x, y}

What I tried getting (incomplete... don't understand the {x, y} part):∀x(x ∈ A → ... )

(c) Problem: A = ø

What I tried getting (don't understand this one, either):∃x(x ¬∈ A)

(d) Problem: A = {x}

What I tried getting (incomplete):∀x(x ∈ A ⇔ ...)

These are the examples given:

(a) Problem: A ⊆ B

Converted to: ∀x(x ∈ A → x ∈ B)

(b) Problem: A ∩ B ≠ ø

Converted to: ∃x(x ∈ A ∧ x ∈ B)

Thanks, your help would be greatly appreciated. :)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Logical Notation

**Physics Forums | Science Articles, Homework Help, Discussion**