Two kinds of quantifiers

Universal quantifier - For all - upside down A

Existential quantifier - There exists - backwards E

To show that there exists – need to find a single example to make it true

To show that for all isn’t true – need a single example to make it false

When using multiple quantifiers together be careful of order - order matters when quantifiers differ

We use letters at the end of the alphabet for “dummy variables” as in “for all x” or “there exists a w” …

In a wff, be careful that your parentheses are in the right place

The parentheses indicate the scope of the quantifier

When you are doing a translation from English to a wff,

For all generally goes with implication

There exists generally goes with AND

A free variable is a variable that is not within the scope of the quantifier.

A wff with a free variable many not have a truth value

A wff with a free variable may have a truth value

There exists is true if I can find 1 example that’s true

For all is false if I can find 1 example that’s false

The word ONLY is going to give us trouble!!!!