Question

fill in the blank,choose the correct logical quantifier in each of the following
answers to choose from: ?,->,<-,<->
1)x=11 __ x is odd
2)f(x) is a continuous funtion__f(x) is a differentiable funtion.
3)The graph of f(x) never touchs the x-axis __f(x)=0 has no real solutions.
4)x=1__x^4=1
5)sin^2=2/4__cos^2=2/4
6)f^1(x)=3x^2__f(x)=x^3
can some one please help me i trying to reivew this hw

Answer 1

For the first one,
If x=11, does that imply x is an odd number? `->`

Think about it the other was as well,
If x is an odd number, does that imply it's the number 11? `<-`

Answer 2

i thought x=11<- x is odd but i got it wrong

Answer 3

See how the arrow is pointing to the left?
That means the second part implies the first part.

So that would read:
If x is an odd number, Then x=11.

That can't be true all the time.
If x is some odd number, it could be something else, right?
Being an odd number doesn't immediately imply that the number is 11.
So it shouldn't be true in that direction.

Answer 4

We wanted `->` for the first one.

If x=11, this implies that x is an odd number. True. :O

Answer 5

The second one is a little harder.
Just something important to remember I guess.

Differentiability implies continuity,
continuity does not necessarily imply differentiability.

`<-`

Answer 6

is 3)<->
4)->
5)->
6)<->
???

Answer 7

were my answer right for 3,4,5,6???