Logical Reasoning - SS2 Mathematics Past Questions and Answers - page 1
The contrapositive of a compound statement \(p \Rightarrow q\) is ______
The inverse of a compound statement \(p \Rightarrow q\) is __
The converse of a compound statement \(p \Rightarrow q\) is ___
Which is a logical equivalent to \(\sim q \Rightarrow \sim p\)?
A compound statement that is always true irrespective of the truth values of its sub statements is a __
contradiction
tautology
contrapositive
inverse
Given:
\[p:He\ is\ very\ hard\ working\]
\[q:He\ is\ very\ intelligent\]
\[r:He\ will\ succeed\]
Give a verb statement that describes each of the following:
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\(p \land q\)
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\(\sim(p \vee q)\)
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\((p \land q) \Rightarrow r\)
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\(r \Rightarrow (q \vee p)\)
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\(p \land q\)
Answer: \(he\ is\ very\ hard\ working\ and\ he\ is\ very\ intelligent\)
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\(\sim(p \vee q)\)
\[\sim(p \vee q) = \sim p \land \sim q\]
Answer: \(he\ is\ not\ very\ hard\ working\ and\ he\ is\ not\ very\ intelligent\)
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\((p \land q) \Rightarrow r\)
Answer: \(if\ he\ is\ very\ hard\ working\ and\ he\ is\ very\ intelligent\ then\ he\ will\ suceed\)
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\(r \Rightarrow (q \vee p)\)
Answer: \(if\ he\ suceeds\ then\ either\ he\ is\ very\ intelligent\ or\ he\ is\ very\ hard\ working\)
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