Decide whether each of the following binary relations is a function. Give a brie

ID: 2849970 • Letter: D

Question

Decide whether each of the following binary relations is a function. Give a brief justification for your answer.

1) Domain: The set of all finite strings of a's and b's.

Rule: (s,z) ? R means that z is the number of a's minus the number of b's in the string s. i.e. (bbaabab, -1) ? R.

Codomain: The set of all binary strings (strings of zeros and ones).

Rule: (n,t) ? R means that the string t begins with exactly n consecutive zeros.

Codomain: The set M of all people alive at midnight, December 31, 1999.

Rule: (z,p) ? R means that person p was z years old at this moment in time.

4) Domain: The set M of all people alive at midnight, December 31, 1999.

Codomain: The set M of all people alive at midnight, December 31, 1999.

Rule: (x,y) ? R means that x and y are siblings.

3) Not a function as it is not one to one. May be more than one person may be aged z years

4) Need not be a function as all persons alive need not have a sibling.

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