Write each of these propositions in the form "p if and only if q" in English. (a) If it is hot outside you buy an ice cream cone, and if you buy an ice cream cone it is hot outside. (b) For you to win the contest it is necessary and sufficient that you have the only winning ticket. (c) You get promoted only if you have connections, and you have connections only if you get promoted. (d) If you watch television your mind will decay, and conversely. (e) The trains run late on exactly those days when I take it.
Write each of these propositions in the form "p if and only if q" in English. (a) If it is hot outside you buy an ice cream cone, and if you buy an ice cream cone it is hot outside. (b) For you to win the contest it is necessary and sufficient that you have the only winning ticket. (c) You get promoted only if you have connections, and you have connections only if you get promoted. (d) If you watch television your mind will decay, and conversely. (e) The trains run late on exactly those days when I take it.
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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![Write each of these propositions in the form "p if and only if q" in English.
(a) If it is hot outside you buy an ice cream cone, and if you buy an ice
cream cone it is hot outside. (b) For you to win the contest it is necessary
and sufficient that you have the only winning ticket. (c) You get promoted
only if you have connections, and you have connections only if you get
promoted. (d) If you watch television your mind will decay, and conversely.
(e) The trains run late on exactly those days when I take it.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5d74132-931e-489d-9d20-d7be2f188ace%2F540c47f7-2835-4731-b4f5-5d521370f8b7%2F2sv8vak_processed.png&w=3840&q=75)
Transcribed Image Text:Write each of these propositions in the form "p if and only if q" in English.
(a) If it is hot outside you buy an ice cream cone, and if you buy an ice
cream cone it is hot outside. (b) For you to win the contest it is necessary
and sufficient that you have the only winning ticket. (c) You get promoted
only if you have connections, and you have connections only if you get
promoted. (d) If you watch television your mind will decay, and conversely.
(e) The trains run late on exactly those days when I take it.
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