Question
In: Advanced Math
The ‘Exclusive OR’ operation (also called XOR) between two propositions p and q is defined as...
The ‘Exclusive OR’ operation (also called XOR) between two propositions p and q is defined as follows:
p ⊕ q = (p ∨ q) ∧ ¬(p ∧ q)
Using laws of propositional logic prove that conjunction distributes over Exclusive OR, i.e, for any proposition r,
r ∧ (p ⊕ q) ≡ (r ∧ p) ⊕ (r ∧ q).
Clearly state which law you are using in each step.
Solutions
Colby Messinger answered 2 years agoRelated Solutions
The ‘Exclusive OR’ operation (also called XOR) between two propositions p and q is defined as...
The ‘Exclusive OR’ operation (also called XOR) between two
propositions p and q is defined as follows:
p ⊕ q = (p ∨ q) ∧ ¬(p ∧ q)
Using laws of propositional logic prove the following:
(i.) Exclusive OR is commutative, i.e., p ⊕ q ≡ q ⊕ p.
(ii.) p ⊕ p is a contradiction.
(iii.) Conjunction distributes over Exclusive OR, i.e, for any
proposition r,
r ∧ (p ⊕ q) ≡ (r ∧ p) ⊕ (r ∧ q)....
Let p and q be propositions. (i) Show (p →q) ≡ (p ∧ ¬q) →F (ii.)...
Let p and q be propositions.
(i) Show (p →q) ≡ (p ∧ ¬q) →F
(ii.) Why does this equivalency allow us to use the proof by
contradiction technique?
Two compound propositions p and q in propositional logic are logically equivalent if . . ..
Complete the following statements.Two compound propositions p and q in propositional logic are
logically equivalent if . . ..An argument form in propositional logic is valid if . . ..A theorem is a statement that . . ..A statement that is assumed to be true is called a(n) . . ..A proof is a valid argument that . . ..
FOR EAICH PAIR OF PROPOSITIONS P AND Q STATE WHETHER ON NOT p=q p=(s→(p ∧¬r)) ∧...
FOR EAICH PAIR OF PROPOSITIONS P AND Q STATE WHETHER ON NOT
p=q
p=(s→(p ∧¬r)) ∧ ((p→(r ∨ q)) ∧ s), Q=p ∨ t
Let p and q be the propositions p:You drive over 65 miles per hour. q: You...
Let p and q be the propositions
p:You drive over 65 miles per hour.
q: You get a speeding ticket.
Write these propositions using p and q and logical
connectives.
a) You do not drive over 65 miles per hour.
b) You drive over 65 miles per hour, but you do not geta
1
speeding ticket.
c) You will get a speeding ticket if you drive over
65 miles per hour.
d) If you do not drive over 65 miles...
The following defines what logical property: A pair of propositions (wffs) P,Q that have the same...
The following defines what logical property: A pair of
propositions (wffs) P,Q that have the same truth value under every
interpretation.
consistency? proposition? argument? equivalence ?
Gene P has two alleles - P and p; gene Q has two alleles - Q...
Gene P has two alleles - P and p; gene Q has two alleles - Q and
q.
If an PQ/pq female is crossed with a
pq/pq male, what percent of the offspring would have
genotype pq/pq if...
A) the genes were completely
linked (no crossing-over at all; recombination frequency =
0; 1 mark)
B) the genes are 10 map units apart (1
mark)
C) the genes are 24 map units apart (1
mark)
For either part (B) or (C)...
Q) A firm has a WACC of 9.60% and is deciding between two mutually exclusive projects....
Q) A firm has a WACC of 9.60%
and is deciding between two mutually exclusive projects. Project A
has an initial investment of $60.12. The additional cash flows for
project A are: year 1 = $19.64, year 2 = $35.94, year 3 = $43.15.
Project B has an initial investment of $74.74. The cash flows for
project B are: year 1 = $57.52, year 2 = $47.69, year 3 = $31.12.
Calculate the Following:
-Payback
Period for Project A:...
Q) A firm has a WACC of 11.15% and is deciding between two mutually exclusive projects....
Q) A firm has a WACC of 11.15% and is deciding between two
mutually exclusive projects. Project A has an initial investment of
$64.25. The additional cash flows for project A are: year 1 =
$16.53, year 2 = $37.29, year 3 = $55.44. Project B has an initial
investment of $74.76. The cash flows for project B are: year 1 =
$58.16, year 2 = $37.08, year 3 = $20.71.
Calculate the Following:
-Payback Period for Project A:
-Payback...
Q) A firm has a WACC of 10.58% and is deciding between two mutually exclusive projects....
Q) A
firm has a WACC of 10.58% and is deciding between two mutually
exclusive projects. Project A has an initial investment of $60.79.
The additional cash flows for project A are: year 1 = $15.60, year
2 = $36.71, year 3 = $41.74. Project B has an initial investment of
$73.28. The cash flows for project B are: year 1 = $59.23, year 2 =
$49.61, year 3 = $23.70. Calculate the Following:
-Payback Period for Project A:...
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