**1**. **a**. There is one function of type {*a*, *b*} → {1}; it maps both *a* and *b* to 1.**c.** There are four functions of type {*a*, *b*} → {1, 2}: one maps both *a* and *b* to 1; one maps both *a* and *b* to 2; one maps *a* to 1 and *b* to 2; and one maps *a* to 2 and *b* to 1.

**2**. **a**. *O*. **c**. {*x* | *x* = 4*k* + 3 where *k* ∈ **N**}. **e.** ∅.

**3**. **a**. *E*. **c**. *E* – {0}. **d**. **N**.

**4**. **a**. −5. **c**. 4.

**6**. For example, *x* = *y* = ½.

**7**. **a**. 3. **c**. 1.

**8**. **a**. 1. **b**. 2. **c**. 3.

**9**. gcd(296, 872) = 8 = (−53) · 296 + 18 · 872.

**10**. **a**. 3. **c.** 3.

**11**. {0, 1, 2, 3, 4, 5, 6}.

**12**. **a**. *f* (∅) = ∅ **c**. *f* ({2, 5}) = {4}. **e**. *f* ({1, 2, 3}) = {0, 2, 4}.

**13**. **a**. 11001. **c**. 1101111.

**14**. **a**. 43. **c**. 2127.

**15**. **a**. floor(*x*) = if *x* ≥ 0 then trunc(*x*) else if *x* = trunc(*x*) then *x* else trunc(*x* − 1).

**16**. When *x* is negative, *f*(*x*, *y*) can be ...

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