Inverse, Contrapositive & indirect proofs Sections 6.2/6.3.
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Transcript of Inverse, Contrapositive & indirect proofs Sections 6.2/6.3.
![Page 1: Inverse, Contrapositive & indirect proofs Sections 6.2/6.3.](https://reader036.fdocuments.in/reader036/viewer/2022082600/5a4d1aed7f8b9ab05997c1ab/html5/thumbnails/1.jpg)
Inverse, Contrapositive & indirect proofsSections 6.2/6.3
![Page 2: Inverse, Contrapositive & indirect proofs Sections 6.2/6.3.](https://reader036.fdocuments.in/reader036/viewer/2022082600/5a4d1aed7f8b9ab05997c1ab/html5/thumbnails/2.jpg)
Converse• Switches hypotheses and
conclusion.Statement: if this is silly then it is
useless.Converse: if this is useless then it
is silly.
![Page 3: Inverse, Contrapositive & indirect proofs Sections 6.2/6.3.](https://reader036.fdocuments.in/reader036/viewer/2022082600/5a4d1aed7f8b9ab05997c1ab/html5/thumbnails/3.jpg)
Inverse• Negates hypotheses and
conclusion.Statement: if this is silly then it is
useless.Converse: if this is not silly then it
is not useless.
![Page 4: Inverse, Contrapositive & indirect proofs Sections 6.2/6.3.](https://reader036.fdocuments.in/reader036/viewer/2022082600/5a4d1aed7f8b9ab05997c1ab/html5/thumbnails/4.jpg)
Contrapositive• Negates and switches
hypotheses and conclusion.Statement: if this is silly then it is
useless.Converse: if this is not useless
then it is not silly.
![Page 5: Inverse, Contrapositive & indirect proofs Sections 6.2/6.3.](https://reader036.fdocuments.in/reader036/viewer/2022082600/5a4d1aed7f8b9ab05997c1ab/html5/thumbnails/5.jpg)
Logically equivalent• Two statements that are always both
true or both false.• A Statement and the contrapositive
are logically equivalent.• The inverse and converse of a
statement are logically equivalent
![Page 6: Inverse, Contrapositive & indirect proofs Sections 6.2/6.3.](https://reader036.fdocuments.in/reader036/viewer/2022082600/5a4d1aed7f8b9ab05997c1ab/html5/thumbnails/6.jpg)
Indirect Proofs
• Assume temporarily that conclusion is not true.• Reason logically until you
reach a contradiction of a known fact