# Working with logic

A true-false statement is any sentence that is either true or false but not both. A negation of a statement has the opposite meaning of a truth value. A negations is written as ~p.

If we call the statement: cucumbers are green, p then:

p: cucumbers are green - this statement is true.

~p: cucumbers are not green - this statement is false.

If we join two statements we can form a compound statement or a conjunction. A conjunction could contain the two statements q and p:

p: cucumbers are green.

q: cucumbers are vegetables.

Conjunctions are noted:

$$p\wedge q$$

This is read - p and q. Cucumbers are green and vegetables.

A conjunction is true only if both statements that form the conjunction is true.

If we have two statements that are joined by "or" we have a disjunction.

**Example**

p: Bill is travelling to Mexico

q: Bill is travelling to Canada

p or q gives us that Bill is travelling to Mexico or Bill is travelling to Canada.

Disjunctions are noted:

$$p\vee q$$

This is read - p or q.

A disjunction is true if at least one of the statements that form it is true.

**Video lesson**

We are given four statements

p: cats have 4 legs (true)

q: hens have 2 legs (true)

r: cats lay egg (false)

t: hens lay egg (true)

Are the following compound statements true or false?

p Λ t

p V r

~p V q

r Λ q

~r V ~q