1. Write each symbolic statement as an English sentence. Use p, q, r, s, and t as defined below. p : Sarah Geronimo is a singer. q : Sarah Geronimo not a songwriter. r : Sarah Geronimo is an actress. s : Sarah Geronimo plays the piano. t : Sarah Geronimo does not play the guitar. (a) (p ∧ q) ∨ r (b) ∼ p → (p ∨ r) (c) (p ∨ s) → (q ∧ t) (d) (r ∧ p) ↔ q (e) t ↔ (∼ r∧ ∼ p)
1. Write each symbolic statement as an English sentence. Use p, q, r, s, and t as defined below. p : Sarah Geronimo is a singer. q : Sarah Geronimo not a songwriter. r : Sarah Geronimo is an actress. s : Sarah Geronimo plays the piano. t : Sarah Geronimo does not play the guitar. (a) (p ∧ q) ∨ r (b) ∼ p → (p ∨ r) (c) (p ∨ s) → (q ∧ t) (d) (r ∧ p) ↔ q (e) t ↔ (∼ r∧ ∼ p)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Write each symbolic statement as an English sentence. Use p, q, r, s, and t
as defined below.
p : Sarah Geronimo is a singer.
q : Sarah Geronimo not a songwriter.
r : Sarah Geronimo is an actress.
s : Sarah Geronimo plays the piano.
t : Sarah Geronimo does not play the guitar.
(a) (p ∧ q) ∨ r
(b) ∼ p → (p ∨ r)
(c) (p ∨ s) → (q ∧ t)
(d) (r ∧ p) ↔ q
(e) t ↔ (∼ r∧ ∼ p)
2. Write each sentence in symbolic form. Use p, q, r and s as defined below.
p : Paul is a table tennis player.
q : Paul is a basketball player.
r : Paul is a rock star.
s : Paul is a mechanical engineer.
(a) Paul is a table tennis player or a basketball player, and he is not an engineer.
(b) If it is not true that Paul is a table tennis player or a rock star, then Paul is a mechanical engineer.
(c) Either Paul is a basketball player and a rock star, or he is a table tennis player.
(d) Paul is a basketball player, if and only if he is not a football player and he is not a rock star.
(e) If Paul is a mechanical engineer, then he is a basketball player and he is not a table tennis player.
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