Purcell 9na Edicion
Enviado por jhcaja • 25 de Agosto de 2014 • 535 Palabras (3 Páginas) • 185 Visitas
0.1 Concepts Review
1. rational numbers
2. dense
3. If not Q then not P.
4. theorems
Problem Set 0.1
1. 4 2(8 11) 6 4 2( 3) 6
4 6 6 16
− − + = − − +
= + + =
2. ( ) [ ]
[ ]
3 2 4 7 12 3 2 4( 5)
3 2 20 3(22) 66
⎡⎣ − − ⎤⎦ = − −
= + = =
3. –4[5(–3 12 – 4) 2(13 – 7)]
–4[5(5) 2(6)] –4[25 12]
–4(37) –148
+ +
= + = +
= =
4. [ ]
[ ] ( )
( )
5 1(7 12 16) 4 2
5 1(3) 4 2 5 3 4 2
5 1 2 5 2 7
− + − + +
= − + + = − + +
= + = + =
5. 5 – 1 65 – 7 58
7 13 91 91 91
= =
6. 3 3 1 3 3 1
4 7 21 6 3 21 6
42 6 7 43
42 42 42 42
+ − = + −
− −
= − + − = −
7. 1 1 1 – 1 1 1 1 3 – 4 1
3 2 4 3 6 3 2 12 6
1 1 – 1 1
3 2 12 6
1 – 1 4
3 24 24
1 3 1
3 24 24
⎡ ⎛ ⎞ ⎤ ⎡ ⎛ ⎞ ⎤ ⎢ ⎜ ⎟ + ⎥ = ⎢ ⎜ ⎟ + ⎥ ⎣ ⎝ ⎠ ⎦ ⎣ ⎝ ⎠ ⎦
⎡ ⎛ ⎞ ⎤ = ⎢ ⎜ ⎟ + ⎥ ⎣ ⎝ ⎠ ⎦
= ⎡ + ⎤ ⎢⎣ ⎥⎦
= ⎛ ⎞ = ⎜ ⎟
⎝ ⎠
8. 1 2 1 1 1 1
3 5 2 3 5 3 2 1 5 3
5 2 15 15
1 2 1 2 1 2 1
3 5 2 15 3 5 15
1 6 1 1 5 1
3 15 15 3 15 9
⎡ ⎛ ⎞⎤ − ⎢ − ⎜ − ⎟⎥ = − ⎣ ⎝ ⎠⎦ ⎡ ⎛ ⎞⎤ ⎢ − ⎜ − ⎟⎥ ⎣ ⎝ ⎠⎦
⎡ ⎛ ⎞⎤ ⎡ ⎤ = − ⎢ − ⎜ ⎟⎥ = − ⎢ − ⎥ ⎣ ⎝ ⎠⎦ ⎣ ⎦
= − ⎛ − ⎞ = − ⎛ ⎞ = − ⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
9.
2 2 2
1 14
3 3
2
14 2 14 2 14 6
21 5 21 21 14
14 3 2 9 6
21 7 3 49 49
⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ = ⎜ ⎟ = ⎜ ⎟ ⎜ − ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠
= ⎛ ⎞ = ⎛ ⎞ = ⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
10.
2 5 2 35 33
7 7 7 7 33 11
1 1 7 1 6 6 2
7 7 7 7
⎛ − ⎞ ⎛ − ⎞ ⎛ − ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎝ ⎠ = ⎝ ⎠ = ⎝ ⎠ = − = −
⎛ − ⎞ ⎛ − ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠ ⎝ ⎠
11.
11 – 12 11 – 4 7 7 21 7 7 7 7
11 12 11 4 15 15
7 21 7 7 7
= = =
+ +
12.
1 3 7 4 6 7 5
2 4 8 8 8 8 8 5
1 3 7 4 6 7 3 3
2 4 8 8 8 8 8
− + − +
= = =
+ − + −
13. 1 3
2 2
1– 1 1– 1 1– 2 3 – 2 1
1 3 3 3 3
...