Register

GATE CSE 2017 Set 2 | Question: 11

• edited by
12,210 views
57 votes
57 votes

Let $p, q, r$ denote the statements ”It is raining”, “It is cold”, and “It is pleasant”, respectively. Then the statement “It is not raining and it is pleasant, and it is not pleasant only if it is raining and it is cold” is represented by

  1. $(\neg p \wedge r) \wedge (\neg r \rightarrow (p \wedge q))$
  2. $(\neg p \wedge r) \wedge ((p \wedge q) \rightarrow  \neg r)$
  3. $(\neg p \wedge r) \vee ((p \wedge q) \rightarrow  \neg r)$
  4. $(\neg p \wedge r) \vee (r \rightarrow (p \wedge q))$
• edited by
User Avatar

10 Answers

1 votes
1 votes

Translation of each formula into english statements :

(p’ $\wedge$ r) :- (not p) and r :- It is not raining and it is pleasant.

r’ → (p $\wedge$ q) :- (If not r, then p and q) $\equiv$ (not r only if p and q) $\equiv$ It is not pleasant only if it is raining and it is cold.

(p $\wedge$ q) → r’ :- (If p and q, then not r) $\equiv$ (p and q only if not r) $\equiv$ It is raining and it is cold only if it is not pleasant.

r → (p $\wedge$ q) :- (If r, then p and q) $\equiv$ (r only if p and q) $\equiv$ It is pleasant only if it is raining and it is cold.

  1. “It is not raining and it is pleasant, and it is not pleasant only if it is raining and it is cold”
  2. “It is not raining and it is pleasant, and it is raining and it is cold only if it is not pleasant”
  3. “Either It is not raining and it is pleasant, or it is raining and it is cold only if it is not pleasant”
  4. “Either It is not raining and it is pleasant, or it is pleasant only if it is raining and it is cold”
User Avatar
0 votes
0 votes

p = ”It is raining”

q =  “It is cold”

r = “It is pleasant”

It is not raining and it is pleasant = ~p ∧ r

x only if y can be written as x→y

 it is not pleasant only if it is raining and it is cold) = ~r→(p ∧ q)

“(It is not raining and it is pleasant), and it is not pleasant only if (it is raining and it is cold)” =   (¬p∧r)∧(¬r→(p∧q))             

So Option A             

 

User Avatar
Page:
Voting & Accepting an answer helps improve the community
Answer:
← PreviousNext →
← Previous in categoryNext in category →

Related questions

30 votes
30 votes
8 answers
1
khushtak asked Feb 14, 2017
9,029 views
GATE CSE 2017 Set 1 | Question: 01
The statement $\left ( ¬p \right ) \Rightarrow \left ( ¬q \right )$ is logically equivalent to which of the statements below? $p \Rightarrow q$ $q \Rightarrow p$ $\left ( ¬q \right ) \vee p$ $\left ( ¬p \right ) \vee q$ I only I and IV only II only II and III only
The statement $\left ( ¬p \right ) \Rightarrow \left ( ¬q \right )$ is logically equivalent to which of the statements below?$p \Rightarrow q$$q \Rightarrow p$$\left ( ...
User Avatar
48 votes
48 votes
10 answers
2
Arjun asked Feb 14, 2017
10,690 views
GATE CSE 2017 Set 1 | Question: 29
Let $p$, $q$ and $r$ be propositions and the expression $\left ( p\rightarrow q \right )\rightarrow r$ be a contradiction. Then, the expression $\left ( r\rightarrow p \right )\rightarrow q$ is a tautology a contradiction always TRUE when $p$ is FALSE always TRUE when $q$ is TRUE
Let $p$, $q$ and $r$ be propositions and the expression $\left ( p\rightarrow q \right )\rightarrow r$ be a contradiction. Then, the expression $\left ( r\rightarrow p \r...
User Avatar
47 votes
47 votes
6 answers
4
Madhav asked Feb 14, 2017
17,941 views
GATE CSE 2017 Set 2 | Question: 30
Consider the recurrence function $T(n) = \begin{cases} 2T(\sqrt{n})+1, & n>2 \\ 2, & 0 < n \leq 2 \end{cases}$ Then $T(n)$ in terms of $\Theta$ notation is $\Theta(\log \log n)$ $\Theta( \log n)$ $\Theta (\sqrt{n})$ $\Theta(n)$
Consider the recurrence function$$T(n) = \begin{cases} 2T(\sqrt{n})+1, & n>2 \\ 2, & 0 < n \leq 2 \end{cases}$$Then $T(n)$ in terms of $\Theta$ notation is$\Theta(\log \l...
User Avatar
Link Copied!