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26.01.2021 •
Mathematics
The diagram below models the layout at a carnival where G, R, C, B, and E are various locations on the grounds. GRPC is a parallelogram.
Part A: Identify a pair of similar triangles
Part B: Explain how you know the triangles for Part A are similar.
Part C: Find the distance from B to E and from P to E. Show your work.
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Ответ:
Vacuous proof is used.
Step-by-step explanation:
Given:
Proposition p(n) :
"if n is a positive integer greater than 1, then n² > n"
To prove:
Prove the proposition p (0)
Solution:
Using the proposition p(n) the proposition p(0) becomes:
p(0) = "if 0 is a positive integer greater than 1, then 0² > 0"
The proposition that "0 is a positive integer greater than 1" is false
Since the premises "if 0 is a positive integer greater than 1" is false this means the overall proposition/ statement is true.
Thus this is the vacuous proof which states that:
if a premise p ("0 is a positive integer greater than 1") is false then the implication or conditional statement p->q ("if n is a positive integer greater than 1, then n² > n") is trivially true.
So in vacuous proof, the implication i.e."if n is a positive integer greater than 1, then n2 > n." is only true when the antecedent i.e. "0 is a positive integer greater than 1" cannot be satisfied.