Question 20 ALL INFORMATION INCLUDED: Part a: Recall the definition of well-formed formulae in propositional logic we co

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Question 20 ALL INFORMATION INCLUDED:
Part a:
Recall the definition of well-formed formulae in propositional
logic we covered in class.
Claim: the following is a well-formed formulae
(p→(q∨T))→q∨v(p→(q∨T))→q∨v
Group of answer choices
True
False
Part b:
Suppose P(n) is a propositional function. Determine for which
positive integers n the statement P(n) must be true, if
Select the one that is correct.
Group of answer choices
all even non-negative integers n
all non-negative integers n
all odd positive integers n
Part c:
Suppose P(n) is a propositional function. Determine for which
positive integers n the statement P(n) must be true, if
Select the one that is correct.
Group of answer choices
all odd positive integers n
all even non-negative integers n
all non-negative integers n
Part d:
What is wrong with the following proof?
Claim: For every nonnegative integer n, 5n=0.
(A) Basis step: 5×0=05×0=0
(B) Inductive step: suppose that 5j =0 for all nonnegative
integers j with 0≤j≤k0≤j≤k.
(C) Write k+1=i+j, where i and j are natural numbers less than
k+1.
(D) By induction hypothesis, 5(k+1)=5(i+j)=5i+5j=0+0=0.
Group of answer choices
A
D
B
C
Part e:
Find the flaw (the claim that does not hold) of the following
proof.
Claim: every postage of three cents or more can be formed using
just three-cent and four-cent stamps.
(A) Basis step: we can form postage of three cents with a single
three cent stamp and we can form postage of four cents using a
single four-cent stamp.
(B) Induction step: assume that we can form postage of j cents
for all nonnegative integers j with j≤kj≤k using just three-cent
and four-cent stamps.
(C) We can then form postage of k+1 cents by replacing one
three-cent stamp with a four-cent stamp or by replacing two
four-cent stamps by three three-cent stamps.
Group of answer choices
A
C
B
Please answer all parts with full work shown, thank you!