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### Transcript of Dec.11 Logical Statements

• Logical Statements
• What type of triangle? why? If the angles of a triangle are all equal, then you have an equilateral triangle.
• A logical argument consists of a premise (hypothesis) and a conclusion. 1. If then statements hypothesis the "if" part conclusion the "then" part known as a "conditional" statement
• Symbolism: p - represents the hypothesis q - represents the conclusion p q This means: if p, then q
• Examples: If the cheque bounced, then there was no money in the account.
• 2. Converse Statement Formed by interchanging the hypothesis and the conclusion. If you have an equilateral triangle, then the angles are all equal. q p **the converse of a statement may or may not be true.**
• 3. If and only if p q is used when the converse of a true statement is true. ex. You have an equilateral triangle "if and only if" the angles are all equal. ex. A triangle has two equal sides "if and only if" it has at least two equal angles.
• 4. Contrapositive reverse and negate the two parts of the original statement if you do not have an equilateral triangle, then the angles are not all equal.
• 5. Inverse statement: you negate the hypothesis and the conclusion, but you don't move them. If the angles of a triangle are not all equal, then you do not have an equilateral triangle.
• If Jeamille lives in Brandon, then Jeamille lives in Manitoba. Write the converse, inverse, and contrapositive statements. Indicate if true. 2. Converse Statement Formed by interchanging the hypothesis and the conclusion.
• 4. Contrapositive reverse and negate the two parts of the original statement
• 5. Inverse statement: you negate the hypothesis and the conclusion, but you don't move them.