1. You receive the following binary message: 1011001. The message includes three check bits.

(a) Which bit was erroneously received?

(b) What was the correct number (in decimal system) sent?

2. Let the functions f: (real numbers) R^# R^# and g: R^# R^# be defined by f(x) = 2x -3 and g(x) = x²+ 5.

Find:

(a) f(5),

(b) g(-3),

(c) g(f(2)) ,

(d) f(g(3)),

(e) g(a-1),

(f) f(g(a-1)),

(g) g(f(x)),

(h) f(g(x+1)), and

(i) g(g(x)).

3. Determine whether the relation R on the set of all people is reflexive, symmetric, anti-symmetric, and/or transitive, where (a, b) R if and only if:

(a) a is taller than b.

(b) a and b were born on the same day.

(c) a has the same first name as b,

(d) a and b have a common grandparent.