# t or f

1. ### Binary operations T/F

1) if * is any binary operation on any set S then a * a = a for all $a \in S$ False 2) If * is any commutative binary operation on any set S, then a*(b*c)=(b*c)*a for all $a,b,c \in S$ True 3) If * is any associative binary operation on any set S, then a*(b*c)=(b*c)*a for all $a,b,c \in S$...
2. ### Is this T/F question "theoretically" right? [Inverse Functions]

Hello, While am preparing questions to teach my cousin inverse functions, I stopped at this T/F question : The inverse function of f(x)=x^4 is f^{-1}(x)=x^{\frac{1}{4}} The answer in the book was "True" Well, the problem is that the given function is not 1-1 so its inverse does not...
3. ### T/F a set containing single vector is lin. indep.

lin indep means that only 0 can be multiplied by the vector to get the 0. I said that this statement is true iff V1 can't equal 0. b) Every linear dependent set conatins the zero vector? this means that c1, c2, and c3 can be multiplied by the v1,v2,v3.... and get the 0 with c1,c2,c3.... not...
4. ### Complex analysis T/F question

Hey, I'm just studying for my exam next week and I've found a few of these true or false problems I'm not 100% with, For the first one, I would say its entire since both functions are entire, and also because the product of two entire functions is entire, so e^xcosy is entire. So...
5. ### T/F on integrals

True of False ? if T prove it, if F give a counter-example. Suppose that f & g are continuous functions on [a,b], then : \int_a^b f(x) \cdot g(x) \, dx \neq \left( \int_a^b f(x) \, dx \right) \cdot \left( \int_a^b g(x) \, dx \right)
6. ### T/F Calculus Questions

T/F Calculus Question If ƒ′(x) has a max value at x = c, then the graph of ƒ(x) has a point of inflection at x = c. i got false
7. ### T/F: If integral f(x) dx is unelementary then integral f(-x) dx is unelementary also

I stucked on this If its true --> Prove. If its false --> Give a counter-example.
8. ### T/F Question on integrals

Answer T/F , if T --> give proof, if F --> give counter-example The definite integral of the product of f and g w.r.t. x DONT EQUAL the product of thier definite integrals with same u/l limits ? I think its false. counter example: f(x) = 0 , g(x) = 0 My answer is correct?
9. ### Dif EQ T/F

State whether the following are true or false. Justify your choice. a.) Given that y = e^{-t}(\cos{t} + \sin{2t}) solves a 2nd order, linear, homogeneous ordinary Dif EQ (ODE), the ODE in equation would be of the form ay'' + by' + cy = 0 where a,b,c \in \mathbb{R} are constants. b.) Given...
10. ### vector space t/f question

T/F prove... a)The intersection of any two subsets of V is a subspace of V b) If V is a vector space other than the zero vector space, then V contains a subpace W such that W doesnt equal V. can sum1 provide a proof for these?