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5 Write each of the following propositions symbolically by first de

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5. Write each of the following propositions symbolically by
first defining p and q.
a. If you study, then you will succeed.
b. If x > 0, then x2 > 0.
c. Kayleigh can go to the movies if Kayleigh does her
homework.
d. If x is odd and y is odd, then xy is odd.
e. If x is odd and y is odd, then x+y is odd.
f. If sets A and B are disjoint, then | A B | = | + | B | .
6. Write the inverse of each propositions in exercise 5.
7. Write the converse if each of the propositions in
exercise 5.
8. Write the contraposition of the proposition in exercise 5.
Use a truth table to determine whether the each argument
is valid 9. p -> q, p -> r/ :. p-> (q r)
Solution
5. Write each of the following propositions symbolically by
first defining p and q.
a. If you study, then you will succeed.
p: You study
q: You will succeed
p -> q
b. If x > 0, then x2 > 0.
p: x>0

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q:x2>0
p -> q
c. Kayleigh can go to the movies if Kayleigh does her
homework.
p:Kayleigh can go to the movies
q:Kayleigh does her homework.
q->p
d. If x is odd and y is odd, then xy is odd.
p:x is odd
q:y is odd
r:xy is odd
(p^q) -> r
e. If x is odd and y is odd, then x+y is odd.
p:x is odd
q:y is odd
r:x+y is odd
(p^q) -> r
f. If sets A and B are disjoint, then | A B | = | + | B | .
p:A is disjoint
q:B is disjoint
r:| A B | = | + | B |
(p^q) -> r
6. Write the inverse of each propositions in exercise 5.
a. If you study, then you will succeed.

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5. Write each of the following propositions symbolically by first defining p and q. a. If you study, then you will succeed. b. If x > 0, then x2 > 0. c. Kayleigh can go to the movies if Kayleigh does her homework. d. If x is odd and y is odd, then xy is odd. e. If x is odd and y is odd, then x+y is odd. f. If sets A and B are disjoint, then | A B | = | + | B | . 6. Write the inverse of each propositions in exercise 5. 7. Write the converse if each of the propositions in exercise 5. 8. Write the contraposition of the proposition in exercise 5. Use a truth table to determine whether the each argument is valid 9. p -> q, p -> r/ :. p-> (q r) Solution 5. Write each of the following propositions symbolically by first defining p and q. a. If you study, then you will succeed. p: You study q: You will succeed p -> q b. If x > 0, then x2 > 0. p: x>0 q:x2>0 p -> q c. Kayleigh can go to the movies if Kayleigh does her homework. p:Kayleigh can go to the movies q:Kayleigh does her homework. q->p d. If x is odd and y is odd, then xy is odd. p:x is odd q:y is odd r:xy is odd (p^q) -> r e. If x is odd and y is odd, then x+y is odd. p:x is odd q:y is odd r:x+y is odd (p^q) -> r f. If sets A an ...
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