Front | Back |
What two steps must you take to find the contrapositive of a conditional statement?
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1. Flip and 2. Negate
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If you are in Central Park, then you are in Manhattan.
Being in Central Park is NECESSARY or SUFFICIENT for being in Manhattan? |
Sufficient
(You could be in Manhattan in other ways than solely being in Central Park). |
If you are in Central Park, then you must be in Manhattan.
Being in Manhattan is NECESSARY or SUFFICIENT for being in Manhattan? |
Necessary
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Symbolize: If you are in Central Park, then you are in Manhattan.
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CP --> M
Contrapositive: NOT M --> NOT CP |
If Mariwyn has the first appointment, Shannon has the fifth appointment.
Mariwyn having the first appoint is NECESSARY or SUFFICIENT to tell you that Shannon has the fifth appointment? |
Sufficient
(Shannon could have the fifth appointment in other circumstances) |
Shannon must have the fifth appointment if Mariwyn has the first appointment.
Shannon having the fifth appointment is NECESSARY or SUFFICIENT for Mariwyn to have the first appointment? |
Necessary
(There is no other way for Mariwyn to have the first appointment). |
Symbolize: If Mariwyn has the first appointment, Shannon has the fifth appointment.
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M1 --> S5
NOT S5 --> NOT M1 |