Logical Reasoning - SS2 Mathematics Past Questions and Answers - page 1

The contrapositive of a compound statement $p \Rightarrow q$ is ______

q \Rightarrow p

\sim p \Rightarrow\sim q

\sim q \Rightarrow\sim p

p \Rightarrow q

Answer & Comments

correct option: c

The inverse of a compound statement $p \Rightarrow q$ is __

q \Rightarrow p

\sim p \Rightarrow\sim q

\sim q \Rightarrow\sim p

p \Rightarrow q

Answer & Comments

correct option: b

The converse of a compound statement $p \Rightarrow q$ is ___

q \Rightarrow p

\sim p \Rightarrow\sim q

\sim q \Rightarrow\sim p

p \Rightarrow q

Answer & Comments

correct option: a

Which is a logical equivalent to $\sim q \Rightarrow\sim p$ ?

q \Rightarrow p

\sim p \Rightarrow\sim q

\sim q \Rightarrow\sim p

p \Rightarrow q

Answer & Comments

correct option: d

A compound statement that is always true irrespective of the truth values of its sub statements is a __

contradiction

tautology

contrapositive

inverse

Answer & Comments

correct option: b

Given:

$p : H e i s v e r y h a r d w o r k i n g$

$q : H e i s v e r y i n t e l l i g e n t$

$r : H e w i l l s u c c e e d$

Give a verb statement that describes each of the following:

Answer & Comments

Answer: $h e i s v e r y h a r d w o r k i n g a n d h e i s v e r y i n t e l l i g e n t$

$\sim (p \lor q) =\sim p \land \sim q$

Answer: $h e i s n o t v e r y h a r d w o r k i n g a n d h e i s n o t v e r y i n t e l l i g e n t$

Answer: $i f h e i s v e r y h a r d w o r k i n g a n d h e i s v e r y i n t e l l i g e n t t h e n h e w i l l s u c e e d$

Answer: $i f h e s u c e e d s t h e n e i t h e r h e i s v e r y i n t e l l i g e n t o r h e i s v e r y h a r d w o r k i n g$