Question

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

Answer 1

What is the solution for iff?

Answer 2

If n is even

Answer 3

then there is an integer k with n = 2k.

Answer 4

ok

Answer 5

i was asking about iff

Answer 6

not the solution...yet

Answer 7

no it is right

Answer 8

huh?

Answer 9

first of all lets take,
if n is even then then the answer of 7n+4 will be even only

Answer 10

first of all...what is iff?

Answer 11

7n+4=7(2k)+4
14k+4=2(7k+2)

Answer 12

ok

Answer 13

if you multiply 7 with any even number you will get the ans as even number only.that is the very valid reason for this.

Answer 14

im asking about iff not the solution @mayankdevnani

Answer 15

im not asking about the solution to this problem.. im just asking what iff is

Answer 16

and adding 4 will does not make any difference to number type whether it is "odd" or "even".

Answer 17

@rambo2210 are you answering my question?

Answer 18

"iff" ?? where is it?

Answer 19

if and only if

Answer 20

im just asking what it means

Answer 21

@lgbasallote ok let me explain you "iff"..

Answer 22

sure

Answer 23

iff means "if and only if"..
it means if "7n+4" will answer the even number then "n" will be even for sure.else it will be odd.

Answer 24

Now you got it?

Answer 25

wait....let me process it

Answer 26

so how is it different from if-then?

Answer 27

If-then is conditional

Answer 28

what about in terms of solution...how is it different from if-then?

Answer 29

post you if-then question here for example.

Answer 30

i think im seeing the difference in wording now (there are two conditions in this case) but anyway...

p = n is even
q = 7n + 4 is even

assume n is even

n = 2k

7n + 4

7(2k) + 4

14k + 4

2(7k + 2)

let 7k + 2 = x

2x

\(\therefore\) 7n + 4 is even when n is even

Answer 31

so how to solve it using biconditional?

Answer 32

what is bi-conditional?

Answer 33

that's what i want to know too

Answer 34

the logical biconditional (sometimes known as the material biconditional) is the logical connective of two statements asserting "p if and only if q", where q is a hypothesis (or antecedent) and p is a conclusion (or consequent).[1] This is often abbreviated p iff q.

Answer 35

well i know that part....what about the solution?

Answer 36

a iff b

=>

if a, then b AND if b, then a

Answer 37

if we prove both directions, we're done

Answer 38

ahh so you prove p -> q and q -> p?

Answer 39

i think so

Answer 40

wonderful

Answer 41

yeap ganeshie8 is rgt.