Introduction:
Syllogism is a type of reasoning that involves drawing conclusions from two given premises.
Syllogism is an important topic in aptitude exams and requires strong logical reasoning skills.
In this blog, we'll cover the basics of syllogism, shortcuts to solve syllogism problems, and examples to help you understand the topic better.
Basics of Syllogism:
A syllogism is a logical argument that consists of two premises and a conclusion.
The premises are statements that are assumed to be true, and the conclusion is a statement that is inferred from the premises.
Syllogisms are used to test logical reasoning skills, and are commonly tested in aptitude exams.
In syllogism, the two premises are given in the form of statements. These statements are classified into three types:
- 1. All A are B
- 2. No A are B
- 3. Some A are B
Using these statements, we can draw conclusions about the relationship between two elements. For example, if we are given the premises "All cats are animals" and "All dogs are animals", we can infer that "Some animals are cats" and "Some animals are dogs".
Shortcuts to Solve Syllogism Problems:
Syllogism problems can be time-consuming and challenging. To solve them quickly and accurately, here are some shortcuts that you can use:
1. Venn Diagrams:
Venn diagrams are a visual representation of the relationship between two or more sets.
To solve syllogism problems, draw a Venn diagram to represent the given premises.
This will help you visualize the relationship between the elements and draw conclusions more easily.
2. Conversion of Statements:
Conversion of statements refers to changing the subject and predicate of each statement.
For example, if we are given the statement "All A are B", we can convert it to "All B are A".
This can help us draw conclusions more easily.
3. Combination of Statements:
A combination of statements refers to combining two or more statements to draw a conclusion.
For example, if we are given the statements "All A are B" and "All B are C", we can combine them to get the conclusion "All A are C".
4. Using Shortcuts and Rules:
There are several rules and shortcuts that can be used to solve syllogism problems quickly and accurately.
These include the following:
- - If one premise is negative, the conclusion must also be negative.
- - If both premises are negative, no conclusion can be drawn.
- - If one premise is universal (i.e. "All" or "No"), the conclusion must also be universal.
- - If both premises are particular (i.e. "Some"), the conclusion must also be particular.
- - If the middle term (i.e. the element that appears in both premises) is distributed in one premise, it must be distributed in the conclusion.
Shortcut Formulas for Syllogism:
Here are some additional shortcut formulas that can be used to solve syllogism problems:
1. All A are B, All B are C => All A are C
2. All A are B, No B are C => No A are C
3. All A are B, Some B are C => Some A are C
4. No A are B, All B are C => No A are C
5. No A are B, No B are C => No A are C
6. No A are B, Some B are C => No A are C
7. Some A are B, All B are C => Some A are C
8. Some A are B, No B are C => No A are C
9. Some A are B, Some B are C => Some A are C
These formulas can be used to quickly determine the relationship between the elements in a syllogism problem and draw conclusions more easily.
Examples of Syllogism Problems:
Here are some examples of syllogism problems and their solutions:
1. All apples are fruits. Some fruits are red. Can we conclude that some apples are red?
Solution:
Yes, we can conclude that some apples are red. The two premises are "All apples are fruits" and "Some fruits are red".
By combining these premises, we can infer that "Some apples are red".
2. No birds can swim. All ducks are birds. Can we conclude that no ducks can swim?
Solution:
Yes, we can conclude that no ducks can swim. The two premises are "No birds can swim" and "All ducks are birds".
By converting the second premise, we get "No birds are ducks".
By combining the two premises, we can infer that "No ducks can swim".
3. Some cats are black. All cats are animals. Can we conclude that some animals are black?
Solution:
Yes, we can conclude that some animals are black. The two premises are "Some cats are black" and "All cats are animals".
By converting the first premise, we get "Some black things are cats". By combining the two premises, we can infer that "Some black animals exist".
4. All dogs are mammals. No fish are mammals. Can we conclude that no dogs are fish?
Solution:
Yes, we can conclude that no dogs are fish. The two premises are "All dogs are mammals" and "No fish are mammals".
By converting the second premise, we get "All fish are non-mammals". By combining the two premises, we can infer that "No dogs are fish".
5. Some trees are tall. All tall things are visible. Can we conclude that some trees are visible?
Solution:
Yes, we can conclude that some trees are visible. The two premises are "Some trees are tall" and "All tall things are visible".
By converting the first premise, we get "Some tall things are trees". By combining the two premises, we can infer that "Some trees are visible".