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"
=======================================
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.
You might be interested in
Answer:
240.
Step-by-step explanation:
Here is the correct question: Three sister are getting new outfits. shirts cost 11 each,skirts coat 25 each and shoes cost 44 a pair. what is the total cost of the new outfits for all of the sisters?
Given: Cost of each shirt is 11
Cost of each skirts coat is 25
Cost of each pair of shoes cost is 44.
Now, finding total cost of shirt, skirt coat and shoes as cost of one new outfit.
=
∴ Total cost of one new outfit is 80.
Next, finding cost of new outfit for all, three sisters.
Cost of new outfit for three sister =
∴ Cost of new outfit for three sister =
240 is the total cost of new outfit for all the sisters.