Mathematical Statements and truth Values

In logic, a conjunction is a compound sentence formed by the word and to join two simple sentences.

The symbol for this is $$ Λ $$. (whenever you see $$ Λ $$ , just read 'and') When two simple sentences, p and q, are joined in a conjunction statement, the conjunction is expressed symbolically as p $$ Λ $$ q.

In logic, a disjunction is a compound sentence formed using the word or to join two simple sentences. The symbol for this is $$ ν $$ . (whenever you see $$ ν $$ read 'or') When two simple sentences, p and q, are joined in a disjunction statement, the disjunction is expressed symbolically as p $$ ν$$ q.
Pneumonic: the way to remember the symbol for disjunction is that, this symbol ν looks like the 'r' in or, the keyword of disjunction statements.

In logic, a conditional statement is compound sentence that is usually expressed with the key words 'If....then...'. Using the variables p and q to represent two simple sentences, the conditional "If p then q" is expressed symbolically as p $$\rightarrow$$ q

Example of a False Conditional

If Clause	Then Clause	Entire Statement
p	q	p q
you are late	you are on time	If you are late, then you are on time.
When p is true	then q is false	The entire statement is false
True	False	False

Warning and Caveat The opposite situation does not lead to a false statement. A false 'if' clause and a true 'then' clause creates a true statement. (Seems counterintuitive at first!) See the table below for an example.

If Clause	Then Clause	Entire Statement
p	q	p q
a human is a cat	then squares have corners	If a human is a cat, then squares have corners.
When p is false	q is true	The entire statement is true.
False	True	True

Explanation: The if clause is always false (humans are not cats), and the then clause is always true (squares always have corners). And the entire statement is true.