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1.) Let A={1,2,3} and B={1,2,3,4}. Let R and S be the relations from A to B whose matrices are given. Compute .
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2.) In each part, sets A and B and a function from A to B are given. Determine whether the function is one to one or onto (or both or neither).
A=|R, B= {x | x is real and x > 0}; f(a)= |a|
3.) Use the universal set U= {a,b,c,….. y, z} and the characteristic function for the specified subset to compute the following function value:
4.) Compute the values indicated. Note that if the domain of these functions is |Z+, then each function is the explicit formula for an infinite sequence. Thus sequences can be viewed as a special type of function.
g(n)= 5-2n
g(14)= ?
5.) Let f be the mod-10 function. Compute f(81).
6.) Let R and S be the given relations from A to B. Compute .
A={a,b,c}; B= {1,2,3}
R= {(a,1), (b,1), (c,2), (c,3)}
S= {(a,1), (a,2), (b,1), (b,2)}
7.) Let f be the mod-10 function. Compute f(1057).
8.) Let A={1,2,3} and B={1,2,3,4}. Let R and S be the relations from A to B whose matrices are given. Compute .
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9.) Assume that
Compute:
10.) Use the universal set U= {a,b,c,….. y, z} and the characteristic function for the specified subset to compute the following function value:
11.) Let R and S be the given relations from A to B. Compute .
A={a,b,c}; B= {1,2,3}
R= {(a,1), (b,1), (c,2), (c,3)}
S= {(a,1), (a,2), (b,1), (b,2)}
12.) Let A={1,2,3} and B={1,2,3,4}. Let R and S be the relations from A to B whose matrices are given. Compute .
,
13.) Use the universal set U= {a,b,c,….. y, z} and the characteristic function for the specified subset to compute the following function value:
14.) Let A= {a,b,c,d} and B= {1,2,3}. Determine whether the relation R from A to B is a function.
R= {(a,3), (b,2), (c,1)}
True or False?
15.) Compute the values indicated. Note that if the domain of these functions is |Z+, then each function is the explicit formula for an infinite sequence. Thus sequences can be viewed as a special type of function.
g(n)= 5-2n
g(4)= ?
