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inna [77]
3 years ago
11

Discrete math

Mathematics
1 answer:
nadya68 [22]3 years ago
6 0

Answer:

1) yes

2) No

3) No

4) yes

5) No

Step-by-step explanation:

1) f(0)=0, f(1)=1, f(2)=2, f(3)=3, then f[\{0, 1, 2, 3\}]=\{0, 1, 2, 3\}

2) f(0)=0, 1^2=1\equiv 1 \text{mod 4}, then f(1)=1; 2^2=4\equiv 0 \text{ mod 4}, then f(2)=0; 3^2=9\equiv 1 \text{mod 4}, then f(3)=1

Then f[\{0, 1, 2, 3\}]=\{0, 1, 3\}, this means that f isn't onto.

3.

  • f(0)=0;
  • 1^1-1=0, then f(1)=0
  • 2^2-2=2, then f(2)=2
  • 3^2-3=6\equiv 2 \text{ mod 4}, then f(3)=2

Then  f[\{0, 1, 2, 3\}]=\{0, 2\}, this means that f isn't onto.

4.  f[\{0, 1, 2, 3\}]=\{0, 1, 2,3\}, then f is onto.

5. f[\{0, 1, 2, 3\}]=\{1, 2\}, this means that f isn't onto.

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Answer:

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