Question

Logical quantifiers
x=5 => x is odd
f(x) is continuous <= f(x) is differentiable
The graph of f(x) never touches x-axis <=> f(x)=0 has no real solutoins
x=1=>x^4=1
sin^2(x)=1/4<=> cos^2(x)=3/4

Answer 1

One of these is wrong for some reason... i dont know which one is wrong

Answer 2

x usually denotes a real number. So I would say if you're talking about REAL 4th roots then the second to last one would be iff?

Answer 3

Or <=> because there is only 1 REAL 4th root to 1, if you don't consider complex. I just feel like complex are always denoted by z. So if the context is real numbers then its <=> imo.

Answer 4

can x =-1?

Answer 5

what i thought is that x^4=1 can => x=1 or x=-1 , but x=1 only yields x^4=1?

Answer 6

Well it depends on how specific you want to be. TECHNICALLY speaking the definition of a square root is:
Suppose s is a positive real number, then r is called the square root of s if r is a positive real number and r^2=s.

Answer 7

So technically speaking for square roots the negative ones "don't count" but realistically speaking, negative numbers square to positive ones.

Answer 8

yea i see where u are going

Answer 9

Every non-negative real number x has a unique non-negative square root, called the principal square root, which is denoted by , where is called radical sign. For example, the principal square root of 9 is 3, denoted , because 32 = 3 × 3 = 9 and 3 is non-negative.

Answer 10

Thats from wikipedia. Ignore where symbols are missing, just copy pasted.

Answer 11

But its just how "technical" you wanna be?

Answer 12

i dont know cuz this is one of my homework..so there were no clearfications..

Answer 13

:/ I'm sorry, I hate things like that.