Answer to Question #183098 in Discrete Mathematics for Maricel

Question

Consider the following statements. Write each statement into its symbolic form.(2 pts each)

Let:

p: Ann solved the problem in discrete math.

q: Bryan solved the problem in discrete math.

r: Cris solved the problem in discrete math.

s: Derynn solved the problem in discrete math.

1. If Derynn solved the problem in discrete math then Bryan and Cris solved it too.

2. Cris solved the problem in discrete math only if Ann and Bryan didn’t solve.

3. Derynn solved the problem in discrete mathematics if and only if Cris solved it and Ann doesn’t solved.

4. If Derynn solved the problem in discrete mathematics, then if Cris doesn’t solve it then Ann solved it.

5. Cris solved the problem in discrete mathematics provided that Derynn doesn’t solved, but if Derynn solved it, then

Bryan doesn’t solve it.

Answer 1

1. If Derynn solved the problem in discrete math then Bryan and Cris solved it too.

$s \to \left( {q \wedge r} \right)$

2. Cris solved the problem in discrete math only if Ann and Bryan didn’t solve.

$r \leftrightarrow \left( {\overline p \wedge \overline q } \right)$

3. Derynn solved the problem in discrete mathematics if and only if Cris solved it and Ann doesn’t solved.

$s \leftrightarrow \left( {r \wedge \overline p } \right)$

4. If Derynn solved the problem in discrete mathematics, then if Cris doesn’t solve it then Ann solved it.

$s \to \left( {\overline r \to p} \right)$

5. Cris solved the problem in discrete mathematics provided that Derynn doesn’t solved, but if Derynn solved it, then Bryan doesn’t solve it.

$\left( {\overline s \to r} \right) \wedge \left( {s \to \overline q } \right)$