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2. a) Define the following with an example: i) Contradiction ii) Proposition b) Show that (pq)^ (p →r) is a Contingency. Use quantifiers to express the statement "if somebody is female and is a parent, then this person is someone's mother

2. a) Define the following with an example: i) Contradiction ii) Proposition b) Show that (pq)^ (p →r) is a Contingency. Use quantifiers to express the statement "if somebody is female and is a parent, then this person is someone's mother

Advanced Engineering Mathematics
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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2. a) Define the following with an example: i) Contradiction ii) Proposition b) Show that (p →q)^(p→r) is a Contingency. c) Use quantifiers to express the statement "if somebody is female and is a parent, then this person is someone's mother d) Let p and q be the propositions: p: I will do every exercise in this book q: I will get an 'A' in this course Write the following propositions using p and q and logical connectives. i) For me to get an 'A' in this course it is necessary and sufficient that I do every exercise in this book. ii) Construct the truth table for your proposition in d(i) above. e) i) Write down the output Boolean expression using p, q and r for the circuit gates below: ii) if p= 1, q = 0 and r= 1 find the output signal for the %3D circuit below:
Transcribed Image Text:2. a) Define the following with an example: i) Contradiction ii) Proposition b) Show that (p →q)^(p→r) is a Contingency. c) Use quantifiers to express the statement "if somebody is female and is a parent, then this person is someone's mother d) Let p and q be the propositions: p: I will do every exercise in this book q: I will get an 'A' in this course Write the following propositions using p and q and logical connectives. i) For me to get an 'A' in this course it is necessary and sufficient that I do every exercise in this book. ii) Construct the truth table for your proposition in d(i) above. e) i) Write down the output Boolean expression using p, q and r for the circuit gates below: ii) if p= 1, q = 0 and r= 1 find the output signal for the %3D circuit below:
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