dec.11 logical statements
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Logical Statements
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What type of triangle?
why?
If the angles of a triangle are all equal, then you have an equilateral triangle.
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A logical argument consists of a premise (hypothesis) and a conclusion.
statements1. If then
hypothesis the "if" part
conclusion the "then" partknown as a "conditional" statement
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Symbolism:
p - represents the hypothesis
q - represents the conclusion
p q
This means: if p, then q
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Examples:
If the cheque bounced, then there was no money in the account.
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2. Converse StatementFormed 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.**
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3. If and only ifis 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.
p q
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4. Contrapositivereverse and negate the two parts of the original statement
if you do not have an equilateral triangle, then the angles are not all equal.
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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.
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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.
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4. Contrapositivereverse and negate the two parts of the original statement
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5. Inverse statement: you negate the hypothesis and the conclusion, but you don't move them.
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