(a) Let p, q, r and s four propositions. Assuming that p and r are false and thatq and s are true, find the truth value of each of the following propositions:i. ((pa¬q)-(qar))→(sv¬q)ii. ((pvq)^(qvs)((¬rvp)^(qvs)(b) Let p and q be two propositions defined as follows: p means 'A student can take the algorithmmodule ' whereas q means 'Student passes discrete mathematics'Express each of the three following compound propositions symbolically by using p, q andappropriate logical symbols.i. 'A sufficient condition for a student to take the algorithm module is that they pass discretemathematics'.ii. 'A student can take the algorithm module only if they pass discrete mathematics'.iii. 'A student can takes the algorithm module if they pass discrete mathematics'.iv. 'A student either passes discrete mathematics or can take the algorithmmodule'.(c) Write in words and express symbolically in terms p and q, defined in (a), the contrapositive, theconverse and the inverse of the implication:A student can take the algorithm module if they pass discrete mathematics(d) Consider the following three propositions: s means "Samir goes to the party "c means "Callum goes to the party"į means "Jay goes to the party".Express each of the three following compound propositions symbolically by using c, j, s andappropriate logical symbols.i. “Samir goes to the party only if both Callum and 'Jay aren't going to the party.ii. "Either both Samir and Jay go to the party or Callum goes to the party, but not both ".(e) A tautology is a proposition that is always true. Let p and q be twopropositions, show that (p - q) (-q - p) is a tautology.

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(a) Let p, q, r and s four propositions. Assuming that p and r are false and that q and s are true, find the truth value of each of the following propositions: i. ((pa¬q)→(qar))→(sv¬q) ii. ((pvq)^(qvs)→((-rvp)^(qvs))

(a) Let p, q, r and s four propositions. Assuming that p and r are false and that q and s are true, find the truth value of each of the following propositions: i. ((pa¬q)→(qar))→(sv¬q) ii. ((pvq)^(qvs)→((-rvp)^(qvs))

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

(a) Let p, q, r and s four propositions. Assuming that p and r are false and that
q and s are true, find the truth value of each of the following propositions:
i. ((pa¬q)-(qar))→(sv¬q)
ii. ((pvq)^(qvs)((¬rvp)^(qvs)
(b) Let p and q be two propositions defined as follows: p means 'A student can take the algorithm
module ' whereas q means 'Student passes discrete mathematics'
Express each of the three following compound propositions symbolically by using p, q and
appropriate logical symbols.
i. 'A sufficient condition for a student to take the algorithm module is that they pass discrete
mathematics'.
ii. 'A student can take the algorithm module only if they pass discrete mathematics'.
iii. 'A student can takes the algorithm module if they pass discrete mathematics'.
iv. 'A student either passes discrete mathematics or can take the algorithm
module'.
(c) Write in words and express symbolically in terms p and q, defined in (a), the contrapositive, the
converse and the inverse of the implication:
A student can take the algorithm module if they pass discrete mathematics
(d) Consider the following three propositions: s means "Samir goes to the party "
c means "Callum goes to the party"
į means "Jay goes to the party".
Express each of the three following compound propositions symbolically by using c, j, s and
appropriate logical symbols.
i. “Samir goes to the party only if both Callum and 'Jay aren't going to the party.
ii. "Either both Samir and Jay go to the party or Callum goes to the party, but not both ".
(e) A tautology is a proposition that is always true. Let p and q be two
propositions, show that (p - q) (-q - p) is a tautology.

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