Answer to Question #246623 in Discrete Mathematics for Neha

Question

3. Let p and q be the propositions "The election is decided" and "The votes have been counted" respectively. Express each of these compound propositions as an English sentence. a) -p b) p Vqc)-p/qd)q-pe)-q→pf) pq g) p→q h)-qV (p^g)

Answer 1

3. Let $p$ and $q$ be the propositions "The election is decided" and "The votes have been counted" respectively.

Let us express each of these compound propositions as an English sentence.

a) It follows that $-p$ denotes the setence "The election is not decided";

b) It follows that $p \lor q$ denotes the setence "The election is decided or the votes have been counted";

c) It follows that $-p\land q$ denotes the setence "The election is not decided and the votes have been counted";

d) It follows that $q\land (-p)$ denotes the setence "The votes have been counted and the election is not decided";

e) It follows that $-q→p$ denotes the setence "If the votes have not been counted, then the election is decided";

f) It follows that $pq$ denotes the setence "The election is decided and the votes have been counted";

g) It follows that $p→q$ denotes the setence "If the election is decided, then the votes have been counted";

h) It follows that $-q\lor (p\land q)$ denotes the setence "The votes have not been counted or the election is decided and the votes have been counted".