Simple math equations, math homework help

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 $f$R^{-1}f$$ .

$f$M_{R}=?egin{bmatrix} 1 & 0 & 1 &0 0 & 0 & 0 &1 1 & 1 & 1 &0 end{bmatrix}f$$ , $f$M_{S}=?egin{bmatrix} 1 & 1 & 1 &1 0 & 0 & 0 &1 0 & 1 & 0 &1 end{bmatrix}f$$

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:

floor

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 $f$R?igcup{S}f$$ .

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 $f$?ar{S}f$$ .

$f$M_{R}=?egin{bmatrix} 1 & 0 & 1 &0 0 & 0 & 0 &1 1 & 1 & 1 &0 end{bmatrix}f$$ , $f$M_{S}=?egin{bmatrix} 1 & 1 & 1 &1 0 & 0 & 0 &1 0 & 1 & 0 &1 end{bmatrix}f$$

9.) Assume that

$f[g(n)=5 - 2nf]$

Compute:

$f[g(129)f]$

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:

floor

11.) Let R and S be the given relations from A to B. Compute $f$S^{-1}f$$ .

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 $f$R?igcup{S}f$$ .
$f$M_{R}=?egin{bmatrix} 1 & 0 & 1 &0 0 & 0 & 0 &1 1 & 1 & 1 &0 end{bmatrix}f$$ , $f$M_{S}=?egin{bmatrix} 1 & 1 & 1 &1 0 & 0 & 0 &1 0 & 1 & 0 &1 end{bmatrix}f$$

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:

floor

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)= ?

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