Answer:
18. The conjecture is: The product of two negative even integers is an even integer.
Testing: Let integers be -4 and -6. [Two negative even integers]
Then (-4) × (-6) = 24 [Even integer]
19. The conjecture is: Sum of two negative odd integers is a negative even integer.
Testing: Let the two negative odd integers be -3 and -7.
Then -3 + (-7) = -10 is a negative even integer
20. The conjecture is: Sum of two even integers and two odd integers is an even integer.
Testing: Let integers be 4, 12, 13, 17 (Two even integers and two odd integers)
Then 4 + 12 + 13 + 17 = 46 (Even integer)
21. The statement is: p------->q [If you ran 1 mile, then you ran 5280 feet]
Decide whether statement is true: So if p is True then q is also True.
Hence p------->q is True. So the given statement is True.
Step-by-step explanation:
18. The product of two negative even integers.
Let the integers be -2m and -2n, m and n are positive integers
Product in (-2m) × (-2n) = 4mn = 2(2mn)
= 2p, p = 2mn
The conjecture is: The product of two negative even integers is an even integer.
Testing: Let integers be -4 and -6. [Two negative even integers]
Then (-4) × (-6) = 24 [Even integer]
19. The sum of two negative odd integers.
Let the integers be -(2m + 1) and -(2n + 1), m and n are positive integers
Then -(2m + 1) + [-(2n + 1)] = -2m - 1 - 2n - 1
= -2m - 2n - 2
= -2(+m + 2 + 1)
= -2p, p = m + n + 1
The conjecture is: Sum of two negative odd integers is a negative even integer.
Testing: Let the two negative odd integers be -3 and -7.
Then -3 + (-7) = -10 is a negative even integer
20. The sum of two even integers and two odd integers.
Let the integers be 2m, 2n, 2p + 1, 2q + 1 (m, n, p, q are positive integers)
Then, 2m + 2n + 2p + 1 + 2q + 1 = 2(m + n + p + q + 1)
= 2r, r = m + n + p + q + 1
The conjecture is: Sum of two even integers and two odd integers is an even integer.
Testing: Let integers be 4, 12, 13, 17 (Two even integers and two odd integers)
Then 4 + 12 + 13 + 17 = 46 (Even integer)
21. Let p: You ran 1 mile
Let q: You 5280 feet
The statement is: p------->q [If you ran 1 mile, then you ran 5280 feet]
Since 1 mile = 5280 feet
So if p is True then q is also True.
Hence p------->q is True. So the given statement is True.
