Prove that if n is a positive integer, then n is even if and only if 7n 4 is even.

1 answer:

3 0

We prove first the direct implication. Assume n is even. Then n = 2k for some integer k. Then 7n + 4 = 14k + 4 = 2(7k + 2), which is even. For the converse, which is â€śif 7n + 4 is even, then n is evenâ€ť, we use a proof by contrapositive. The contrapositive is: â€śif n is not even (that is, odd), then 7n + 4 is not even (that is, odd) If n is odd, then n = 2k + 1, for some integer k. Then 7n + 4 = 14k + 11 = 2(7k + 5) + 1, which is odd.

You might be interested in

Jon ran 5 1/2 miles twice this week. How many miles did he run total?

wlad13 [49]

Answer:

Step-by-step explanation:

5 1/2 x 2= 11

5 0

3 years ago

Quadrilateral ABCD is located at A (−2, 2), B (−2, 4), C (2, 4), and D (2, 2). The quadrilateral is then transformed using the r

Mademuasel [1]

New cordinates are formed by adding 7 in x and subtracting 2 from y
A(−2, 2) =A ' (-2 +7 , 2 - 1 ) = A' (5,1)
B(−2, 4) = B' (-2 + 7 , 4 -1 )= B' (5,3)
C(2, 4) = C' (2 + 7 , 4 -1 )= C' (9,3)
D(2, 2) D' (2 + 7 , 2 -1 ) = D' ( 9 , 1)

8 0

2 years ago

Name the property the equation illustrates.

kykrilka [37]

You can multiply the equation in any order.

2[-3/9]=[-3/9]2

Commutative Property of Multiplication

4 0

2 years ago

Classify the decimal forms of 3/12 and and 2/9 as repeating or as repeating or terminating.

andre [41]

Answer:

3/12: terminating; 2/9: repeating

Step-by-step explanation:

3/12=0.25 terminating as it has a finite number of digits after the decimal point.

2/9=0.222.... repeating decimal as its number is repeated indefinitely.

6 0

3 years ago

How to show that a function is surjective?

photoshop1234 [79]

Algebra formula based function

6 0

2 years ago