Proof by Contradiction


How do you show an argument is valid by contradiction?

	1. assume the conclusion is false (negate the conclusion)
	2. add the negated conclusion to the premises
	3. apply inference rules to arrive at a contradiction
	4. conclude the assumption was wrong and the conclusion is true


















Prove the argument using proof by contradiction.

	There is an undeclared variable or
	there is a syntax error.
	If there is a syntax error,
	there is a missing semicolon or
	a variable name is misspelled.
	There is not a missing semicolon.
	There is not a misspelled variable name.
	Therefore there is an undeclared variable.

	U  undeclared variable
	E  syntax error
	S  missing semicolon
	M  misspelled variable name


















Classwork
You may work with a partner.

Prove the argument using proof by contradiction.

	If the house is next to a lake,
	the treasure is not in the kitchen.
	If the tree in the yard is an elm,
	the treasure is in the kitchen.
	The house is next to a lake.
	The tree in the yard is an elm or
	the treasure is buried under the flagpole.
	Therefore the treasure is under the flagpole.

	L  house is next to lake
	K  treasure is in kitchen
	E  tree is an elm
	P  treasure is under flagpole