questionr
Early access
Exams
Joint Entrance Examination
Mathematics
Mathematical Reasoning
Question 93
Question 93 of 103
Medium
MCQ
Let p and q be two statements. Then \[ \sim \left( {p \wedge (p \Rightarrow \, \sim q)} \right)\] is equivalent to
A
\[\left( { \sim p} \right) \vee q\]
B
\[p \vee \left( {p \wedge ( \sim q)} \right)\]
C
\[p \vee \left( {p \wedge q} \right)\]
D
\[p \vee \left( {\left( { \sim p} \right) \wedge q} \right)\]
Check answer
Press A-D to select · Enter to check
Solutions · 1
Post your solution
Official solution
Making truth table
(
E
≡
∼
(
p
∧
(
p
⇒
∼
q
)
)
(E \equiv \sim(p \wedge(p \Rightarrow \sim q))
(
E
≡∼
(
p
∧
(
p
⇒∼
q
))
p
p
p
q
q
q
∼
p
\sim p
∼
p
∼
q
\sim q
∼
q
p
∨
q
p \vee q
p
∨
q
p
∧
q
p \wedge q
p
∧
q
p
⇒
p
∼
q
\begin{aligned}p \Rightarrow p \sim q\end{aligned}
p
⇒
p
∼
q
p
∧
(
p
⇒
∼
q
)
p \wedge (p \Rightarrow \sim q)
p
∧
(
p
⇒∼
q
)
E
\mathrm{E}
E
T
\mathrm{T}
T
T
\mathrm{T}
T
F
\mathrm{F}
F
F
\mathrm{F}
F
T
\mathrm{T}
T
T
\mathrm{T}
T
F
\mathrm{F}
F
F
\mathrm{F}
F
T
\mathrm{T}
T
T
\mathrm{T}
T
F
\mathrm{F}
F
F
\mathrm{F}
F
T
\mathrm{T}
T
T
\mathrm{T}
T
F
\mathrm{F}
F
T
\mathrm{T}
T
T
\mathrm{T}
T
F
\mathrm{F}
F
F
\mathrm{F}
F
T
\mathrm{T}
T
T
\mathrm{T}
T
F
\mathrm{F}
F
T
\mathrm{T}
T
F
\mathrm{F}
F
T
\mathrm{T}
T
F
\mathrm{F}
F
T
\mathrm{T}
T
F
\mathrm{F}
F
F
\mathrm{F}
F
T
\mathrm{T}
T
T
\mathrm{T}
T
F
\mathrm{F}
F
F
\mathrm{F}
F
T
\mathrm{T}
T
F
\mathrm{F}
F
T
\mathrm{T}
T
&
\&
&
∼
p
∨
q
\sim p \vee q
∼
p
∨
q
p
∨
(
∼
p
∧
q
)
p \vee(\sim p \wedge q)
p
∨
(
∼
p
∧
q
)
p
∨
(
p
∧
q
)
p \vee(p \wedge q)
p
∨
(
p
∧
q
)
p
∨
(
p
∧
∼
q
)
p \vee(p \wedge \sim q)
p
∨
(
p
∧
∼
q
)
T
\mathrm{T}
T
T
\mathrm{T}
T
T
\mathrm{T}
T
T
\mathrm{T}
T
F
\mathrm{F}
F
T
\mathrm{T}
T
T
\mathrm{T}
T
T
\mathrm{T}
T
T
\mathrm{T}
T
T
\mathrm{T}
T
F
\mathrm{F}
F
F
\mathrm{F}
F
T
\mathrm{T}
T
F
\mathrm{F}
F
F
\mathrm{F}
F
F
\mathrm{F}
F
∴
∼
(
p
∧
(
p
⇒
∼
q
)
)
\therefore \sim(p \wedge(p \Rightarrow \sim q))
∴
∼
(
p
∧
(
p
⇒∼
q
))
is equivalent to
∼
p
∨
q
\sim p \vee q
∼
p
∨
q
Other Method : \[ \sim \left( {p \vee \left( {p \to \sim q} \right.} \right)\] \[ = \sim p \vee \sim \left( {p \to \sim q} \right)\] \[ = \sim p \vee \sim \left( { \sim p \vee \sim q} \right)\] \[= \sim p \vee \left( {p \wedge q} \right)\] \[ = \left( { \sim p \vee p} \right) \wedge \left( { \sim p \vee q} \right)\] \[ = t \wedge \left( { \sim p \vee q} \right)\] \[ = \sim p \vee q\]
Answer the question to unlock
Previous
Next