1) let P denote the positive real numbers excluding 0, which of the following de
ID: 2961691 • Letter: 1
Question
1) let P denote the positive real numbers excluding 0, which of the following defines a function f: P -> P which is one to one but NOT onto?
a. 1/(1+ x^2)
b. 1/x
c. x
d. x^2
e. x^2 - 2x + 2
2) which of the following formula for x * y defines an associative operation on the nonzero real numbers?
a) x/y
b) x + y
c) x - y
d) xy + 1
e) absolute value of y
3) let a = ( 1 2 3 4) and b = ( 1 3 4). what is (a inverse)b ?
a)(1 2)
b) (2 3)
c) (1 2 3)
d) ( 2 3 4)
e) ( 1 2 4)
4) which of the following is a subgorup of S4?
a) all 2 cycles and (1)
b) all 3 cycles and (1)
c) all 4 cycles and (1)
d) (1), (12)(34), (13)(24), (14)(23)
5)For a group G let G^3 denote all elements of the form g^3 where g is in G. For which group G is G^3 NOT a subgroup?
a)S2
b)S3
c)A3
d)A4
Explanation / Answer
1.) d.) x^2
for f(x) = x^2
it is clearly one-one because for every unique x there is a unique x^2 in the domain P
it is not onto because it does not include non-square positive real numbers.
2.) a) x/y
it is associative because x/y = (1/y)*x
3.) e) ( 1 2 4)
for a = ( 1 2 3 4) and b = ( 1 3 4)
(a inverse)b = (1 2 4)
4) d) (1), (12)(34), (13)(24), (14)(23)
5) d)A4
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