Use a proof by contradiction to prove that the sum of two odd integers is even.
1 answer:
Answer:
Step-by-step explanation:
to prove that the sum of two odd integers is even.
Let a and b be two odd integers.
If possible assume that
, i.e. sum is a product of 2, hence even.
Since a is odd,
for some integer k.
Subtract a from a+b to get
i.e. b is a multiple of some integer l by 2
i.e. b is even.
This contradicts our assumption that both a and b are odd
Hence proved that the sum of two odd integers is even.
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Answers with Explanation.
i. If we raise a number to an exponent of 1, we get the same number.
ii. If we raise 10 to an exponent of 2, it means we multiply 10 by itself two times.
iii. If we raise 10 to an exponent of 3, it means we multiply 10 by itself three times.
iv. If we raise 10 to an exponent of 4, it means we multiply 10 by itself four times.
v. If we raise 10 to an exponent of 5, it means we multiply 10 by itself five times.
vi. Recall that,
We apply this law of exponents to obtain,
vii. We apply
again to obtain,
i. If we raise a number to an exponent of 1, we get the same number.
ii. If we raise 10 to an exponent of 2, it means we multiply 10 by itself two times.
iii. If we raise 10 to an exponent of 3, it means we multiply 10 by itself three times.
iv. If we raise 10 to an exponent of 4, it means we multiply 10 by itself four times.
v. If we raise 10 to an exponent of 5, it means we multiply 10 by itself five times.
vi. Recall that,
We apply this law of exponents to obtain,
vii. We apply
again to obtain,