# 1.3 – The Look and Language of Logic

## Objectives

• Explore Venn diagrams as representations of conditional statements.
• Investigate the converse, inverse, and contrapositives of conditional statements.
• Use the basic symbols of logic to write conditional statements in shorthand.
• Use syllogisms to form chains of (or make connections between) ideas.

## Key Terms

• contrapositive – a statement in the form “If not B, then not A,” given the statement “If A, then B.”
• converse – a statement in the form “If B, then A,” given the statement “If A, then B.”
• Counterexample – an exception to a proposed general rule or law
• inverse – a statement in the form “If not A, then not B,” given the statement “If A, then B.”
• syllogism – a form of deductive reasoning that combines two or more related conditional statements in order to arrive at a conclusion.
• Venn diagram – a diagram that uses two or more circles or other shapes to represent sets. Elements that belong to more than one set are placed in the areas where the circles overlap.

## Notes

Rules of Logic
• For a statement to be true, it must be true for every possible case.
• A statement is only TRUE if there are NO exceptions.
• For a statement to be false, it must be false in at least one possible case.
• A statement is FALSE even if there is ONLY ONE exception.

Language of Logic
• Venn diagrams can be used to represent conditional logic.  Watch the video below.

(Apex Learning, 2015)

• Summary
• Remember: IF statements go on the INSIDE of Venn diagrams!

(Apex Learning, 2015)

(Apex Learning, 2015)

(Apex Learning, 2015)

• Shorthand symbols

(Apex Learning, 2015)

• Summary

(Apex Learning, 2015)

• Examples

(Apex Learning, 2015)

• Syllogism: a chain of conditional statements.
• In the chain, the first and last statements combine to make up the conclusion.

(Apex Learning, 2015)

• Watch the video (below) that shows how to write the conclusion of a syllogism.

• Example
• If I eat pie, then I will be happy.  If I am happy, then I will do my homework.  If I do my homework, then I will get my degree.  If I get my degree, then I will get a good job!  So, if I eat pie, then I will get a good job!
• Shorthand
• $p\implies h$ and
• $h\implies w$ and
• $w\implies d$ and
• $d\implies j$
• So, in conclusion, $p\implies j$.