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Odd number of digits in a palindrome to be divisible by 11?
No, not necessarily. 121 is a palindrome number with 3 digits (odd) and is divisible by 11. So this satisfies the premise, but 101, 111, 131, etc are not divisible by 11.An example which satisfies the premise does not prove it true, but one which contradicts the premise is enough to prove it false.
Is it true or false that the cosine function is an odd function?
False; the cosine function is an even function as cos(-x) = -cos(x).
If a premise and the conclusion are true the argument is true?
Not necessarily. An argument is not automatically true just because the premise and conclusion are true. The reasoning connecting the premise to the conclusion must also be valid for the argument to be considered true.
What does negate the premise mean?
A premise is the fact or supposition upon which a chain of logic is based. If it is true, and logic (reasoning) is correctly applied, then the conclusion reached by the chain of logic is also true. When you negate the premise, you show that the premise is not true and that, therefore, the conclusion is not true, or at the least, has not been demonstrate to be true.
How is the function x plus sin x best described?
It is an increasing odd function.
Is the sine functions an odd function?
Yes. Along with the tangent function, sine is an odd function. Cosine, however, is an even function.
How a function is even and odd?
The only way a function can be both even and odd is for it to ignore the input, i.e. for it to be a constant function. e.g. f(x)=4 is both even and odd. An even function is one where f(x)=f(-x), and an odd one is where -f(x)=f(-x). This doesn't make sense. Let's analyze. For a function to be even, f(-x)=f(x). For a function to be odd, f(-x)=-f(x). In this case, f(x)=4, and f(-x)=4. As such, for the first part of the even-odd definition, we have 4=4, which is true, making the function even. However, for the second part of it, we have 4=-4 (f(-x)=4, but -f(x)=-4), which is not true. Therefore constant functions are even because f(-x)=f(x), but not odd because f(-x)!=-f(x).
Why is the secant function is an even function and the tangent and cosecant are odd functions?
I find it convenient to express other trigonometric functions in terms of sine and cosine - that tends to simplify things. The secant function is even because it is the reciprocal of the cosine function, which is even. The tangent function is the sine divided by the cosine - an odd function divided by an even function. Therefore it is odd. The cosecant is the reciprocal of an odd function, so it is naturally also an odd function.
The sum of 3 odd numbers is odd-true or false?
True.
Is the Sine function an odd function?
Yes
What are even and odd functions?
An even function is a function that creates symmetry across the y-axis. An odd function is a function that creates origin symmetry.
Is signum function an odd or even function?
both
