# Number Of Reflexive & Symmetric Relations On Set S with n Elements

Suppose S is a set with n elements.

(a) How many relations are there on S?

There are relations on S.

(b) How many reﬂexive relations are there on S?

There are reflexive relations on S.

(c) How many symmetric relations are there on S?

There are reflexive relations on S.

(d) How many relations are there on S that are both reﬂexive and symmetric?

There are reflexive & symmetric relations on S.

# Question about Set Descriptions

Write formal descriptions of the following sets

(a) The set containing the numbers 1, 10, 100:

{1, 10, 100}

(b) The set containing all integers greater than 5:

{n ε Z | n > 5}

(c) The set containing all natural numbers that are less than 5:

{n ε N | n < 5}

(d) The set containing the string aba:

{aba}

(e) The set containing the empty string:

{ε}

(f) The set containing nothing:

Ø

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