Select the option, which is the logical equivalent of the statement given below: It is not true that both Hyderabad and Bangalore are in India.
Hyderabad is in India or Bangalore is in India.
Understanding the Statement
The given statement is: "It is not true that both Hyderabad and Bangalore are in India."
This statement involves a negation and a conjunction (the idea of "both"). Let's break it down using simple logical representation.
Representing Statements Logically
Let's define two simple statements:
- Let P be the statement: "Hyderabad is in India."
- Let Q be the statement: "Bangalore is in India."
The phrase "both Hyderabad and Bangalore are in India" is a conjunction of P and Q, which can be written as $P \land Q$.
The original statement says "It is not true that (both Hyderabad and Bangalore are in India)". This means the negation of the conjunction $(P \land Q)$.
In logical symbols, the original statement is represented as $\neg (P \land Q)$.
Analyzing the Options
We need to find the logical equivalent of $\neg (P \land Q)$ among the given options.
Let's look at the structure of the provided options:
- "Hyderabad is in India or Bangalore is in India." This is $P \lor Q$.
- "Hyderabad is not in India and Bangalore is not in India." This is $\neg P \land \neg Q$.
- "Hyderabad is not in India and Bangalore is in India." This is $\neg P \land Q$.
- "Hyderabad is in India and Bangalore is not in India." This is $P \land \neg Q$.
Finding the Logical Equivalent
The original statement is $\neg (P \land Q)$. This means the situation where both P and Q are true is false. The statement is true in all other cases.
Based on the provided options, we need to select the one that is considered logically equivalent to $\neg (P \land Q)$. The provided correct answer corresponds to Option 1, which is $P \lor Q$.
Let's examine Option 1: "Hyderabad is in India or Bangalore is in India". This statement ($P \lor Q$) is true if at least one of P or Q is true (including the case where both are true).
Comparing the original statement $\neg (P \land Q)$ and Option 1 ($P \lor Q$), the provided solution indicates that $P \lor Q$ is the logical equivalent.
Conclusion
The original statement "It is not true that both Hyderabad and Bangalore are in India" is represented as $\neg (P \land Q)$.
Based on the options provided and the designated correct answer, the logical equivalent is considered to be "Hyderabad is in India or Bangalore is in India", which is represented as $P \lor Q$.
Therefore, the option that is the logical equivalent is "Hyderabad is in India or Bangalore is in India."
Important Questions from Critical Reasoning
In this question, a passage is given followed by a statement. Read the passage carefully and judge the statement based on the given passage.
Over three lakh birds of different species have arrived in Kashmir valley, according to wildlife warden wetlands of Kashmir, Rouf Zargar. Usually every year, approximately 9 lakh birds migrate to the valley from different cold habitats of the world. Therefore, the valley witnesses new species of birds every year. Birds can go any place depending upon the leading flock. Kashmir is comparatively less cold than their own natural habitat which makes birds to start migrating to the valley in September every year.
The birds can help in increasing tourism in the valley. Shikara owner Bashir Ahmad said, "Since tourism in valley is not gaining its pace in valley after 2016 turmoil, these migratory birds can attract tourist from across the globe, if tourism department can project them in planned way, and advertise at big level, definitely it will help to boost tourism in valley"
Statement:
Birds migrate to Kashmir valley as it is colder compared to their natural habitat.
Choose the appropriate one from the following options
A -The statement is definitely true
B -The statement is probably true
C -The statement is cannot be determined
D -The statement is definitely false
- Statement:
The cross cultural social work implies the interaction between one culture and a client of another culture.
Conclusion:
It enables the professional social work for effective intervention of cross cultural diversity management. - Among the following propositions two are related in such a way that one is the denial of the other. Which are those propositions?
Propositions:
(a) All elephants are equal to cats
(b) Some elephants are not equal to cats
(c) Some elephants are equal to cats
(d) Few elephants are also equal to cats Consider the given statement and decide which of the given assumptions is/are implicit in the statement.
Statement:
Indians go abroad to get better jobs.
Assumptions:
1. Indians can get better jobs abroad.
2. India lacks better job opportunities.
Human beings always have _______.
