13675681
Description
Mind Map by Nur Aisyah, updated more than 1 year ago
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Created by Nur Aisyah
over 7 years ago
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Mathematical Reasoning
- Statement
- Compound Statement
- and
- both statements
true?
- true
- yes
- true
- both statements
true?
- or
- at least one
statement is true?
- true
- yes
- true
- at least one
statement is true?
- false
- no
- no
- no
- and
- A statement that is
either true or false but
not both
- The process of changing the truth
value of a statement using the word
"not" or "no" is known as negation.
- Compound Statement
- Quantifiers
- ALL - To show that every objects
satisfies certain conditions
- SOME - To show that one or
more objects satisfy certain
conditions
- ALL - To show that every objects
satisfies certain conditions
- Implications
- "p if and only if q"is a
combination of two
implications.
- ® Implication 1 : "if p, then q"
® Implication 2 : "if q, then p"
- ® Implication 1 : "if p, then q"
® Implication 2 : "if q, then p"
- Truth value of the converse of an
implicationThe converse of an
implication is not necessarily true.
- if q then p
- q = antecedent
- p = consequent
- p = consequent
- q = antecedent
- if p then q
- p = antecedent
- q = consequent
- q = consequent
- p = antecedent
- converse
- p if and only if q
- "p if and only if q"is a
combination of two
implications.
- Arguments
- FORM I
- All A are B
- C is A
- C is B
- C is B
- C is A
- All A are B
- FORM II
- If p then q
- P is true
- q is true
- q is true
- P is true
- If p then q
- FORM III
- If p then q
- q is not true
- p is not true
- p is not true
- q is not true
- If p then q
- FORM I
- Deduction and Induction
- Deduction is the process of
making a specific conclusion
based on a general statement.
- Making conclusion by deductionThrough
reasoning by deduction ,we can make
conclusion for a specific case based on a
general statement.
- Making conclusion by deductionThrough
reasoning by deduction ,we can make
conclusion for a specific case based on a
general statement.
- Induction is the process of
making a general conclusion
based on specific cases
- Making generalisations by induction.Through
reasoning by induction,we can make
generalisation based on the pattern of a
numerical sequence.
- Making generalisations by induction.Through
reasoning by induction,we can make
generalisation based on the pattern of a
numerical sequence.
- Deduction is the process of
making a specific conclusion
based on a general statement.
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