MAT 243 WRITTEN HOMEWORK 1
(1) Fill in the blank in the statements below:
(a) Two propositions are logically equivalent if and only if they have the same truth values.
(b) A tautology is a proposition that is always true
(c) The negation of ”if
p
then
q
” is
p
∧ ¬
q
(d) ”
r
is a sufficient condition for
s
” means if
r
then
s
.
(e) ”
a
is a necessary condition for
b
” means if
b
then
a
.
(2) Given the conditional:
I go to the beach or I go out dancing, if I am done with my work.
(a) State the converse of this statement:

(b) State the contrapositive of this statement:

(c) State the negation of this statement:

(3) Write the following statements in symbolic form. Identify the propositional functions (if
needed), universe of discourse you are using:

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