I need help with truth tables
1 answer:
Part A
The conditional is "if the angles are vertical, then the angles are congruent"
The inverse is "If the angles are not vertical, then the angles are not congruent"
The converse is "If the angles are congruent, then the angles are vertical"
The contrapositive is "If the angles are not congruent, then the angles are not vertical"
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Part B
If the original conditional is true, then the contrapositive is also true. This is because the original conditional and contrapositive have the same identical truth tables (see attached). Similarly, the inverse and converse have identical truth tables (again see attached).
Alternatively, you can think of the original conditional P --> Q as ~P v Q which flips to Q v ~P and then that turns into ~Q -> ~P showing how P -> Q is the same as ~Q -> ~P, but I'm not sure if you've learned about these algebraic properties yet. Its probably best to stick to the truth tables.
The conditional is "if the angles are vertical, then the angles are congruent"
The inverse is "If the angles are not vertical, then the angles are not congruent"
The converse is "If the angles are congruent, then the angles are vertical"
The contrapositive is "If the angles are not congruent, then the angles are not vertical"
=======================================
Part B
If the original conditional is true, then the contrapositive is also true. This is because the original conditional and contrapositive have the same identical truth tables (see attached). Similarly, the inverse and converse have identical truth tables (again see attached).
Alternatively, you can think of the original conditional P --> Q as ~P v Q which flips to Q v ~P and then that turns into ~Q -> ~P showing how P -> Q is the same as ~Q -> ~P, but I'm not sure if you've learned about these algebraic properties yet. Its probably best to stick to the truth tables.
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