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
Identifying Denying Propositions
The question asks us to find two propositions from the given list that are denials of each other. In logic, two statements are denials (contradictories) if they cannot both be true and cannot both be false simultaneously. If one is true, the other must be false.
Analyzing Propositions
Let's analyze the logical form of each proposition:
- (a) All elephants are equal to cats: This is a universal affirmative statement. Standard form: All S are P.
- (b) Some elephants are not equal to cats: This is a particular negative statement. Standard form: Some S are not P.
- (c) Some elephants are equal to cats: This is a particular affirmative statement. Standard form: Some S are P.
- (d) Few elephants are also equal to cats: "Few" implies "some". So, this is also a particular affirmative statement, equivalent to (c). Standard form: Some S are P.
Finding the Denial Pair
We need to find a pair that represents contradiction:
- The contradictory of a universal affirmative statement ("All S are P") is a particular negative statement ("Some S are not P").
- Applying this, the contradictory of proposition (a) "All elephants are equal to cats" is "Some elephants are not equal to cats", which is proposition (b).
Let's check the relationships:
- Pair (a) and (b): "All elephants are equal to cats" (A form) and "Some elephants are not equal to cats" (O form). These are contradictories.
- Pair (a) and (c): "All elephants are equal to cats" (A form) and "Some elephants are equal to cats" (I form). These are not contradictories.
- Pair (c) and (d): Both are "Some elephants are equal to cats" (I form). They are essentially the same statement, not denials.
Therefore, propositions (a) and (b) are denials of each other.
Conclusion
The propositions that are denials of each other are (a) and (b).
Similar Questions
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.
Read the given statements carefully and answer the question.
Statement:
A leading tennis star who faced media after failing a dope test said, "I don't want to end my career this way. I hope I will be given another chance to play this game. I let the sport down.
" Which of the following is true according to the given statement?
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. 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 _______.
What does a mirror always do?
Select the correct option.
