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Find the domain and range of f of x equals x squared minus 4?
D = {x [element of reals]}R = {y [element of reals]|y >= 4}
How many two elements subsets does a 4 element set have?
6
How do you do boolean algebra?
It is used in science and proofs of proofs in maths, taking an example: Hypothesis: Bananas are red. (There exists) x x (is an element of) Red (and) Banana Banana (implies) Red (not) Red (implies) (not) Banana If a yellow banana is found, (There exists) y y(is an element of)Banana (therefore) y(is an element of) Red There is a contradiction, as the banana must be red, but it is yellow. The above is not the only use, but Boolean algebra exclusively contains symbols of (not), (and), and (or).
What is the order of an element of a group?
The order of a group is the same as its cardinality - i.e. the number of elements the set contains. The order of a particular element is the order of the (cyclic) group generated by that element - i.e. the order of the group {...a-4, a-3, a-2, a-1, e, a, a2, a3, a4...}. If these powers do not go on forever, it will have a finite order; otherwise the order will be infinite.
When the additive inverse of a number equal to the absolute value of the number?
One example would be a Galois Field size 4 (ie GF(4)). Here, the elements are {0,1,2,3} and every element is its own additive inverse.
