1. 1. Logical ReasoningLogical Reasoning SyllogismSyllogism A syllogism is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true. Wikipedia contributors. "Syllogism." Wikipedia, The Free Encyclopedia. 7 Jun. 2015. Web. 14 Jun. 2015.
2. 2. Syllogism ??? There will be 'statements' and 'conclusions' . The challenge is to check whether the given conclusions are valid to the given statements.
3. 3. Cases of statementsCases of statements 1.All 2.Some 3.All ... Some 4.Some ... All 5.No
4. 4. Case 1: All Statements: All papers are scissors All scissors are rocks The possible conclusions for the above said statements can be represented in a diagram as Here the yellow cirlce represents all papers, red all scissors and green all rocks.
5. 5. The possible conclusions are From inner circle to the outer circle, we can say the following conclusions 1.All papers are scissors 2.All papers are rocks 3.All scissors are rocks Looking from outer circle to the inner circle, we can say 4.Some rocks are scissors 5.Some rocks are papers 6.Some scissors are papers.
6. 6. Case 2: Some Statements: Some rocks are papers Some papers are scissors The possible conclusions can be pictorised in 2 possible way Note: As far as there is no statement like No rocks are scissors , the second diagram is also a possibility.
7. 7. Case 3: All ... Some Statements: All rocks are papers Some papers are lizard The possible conclusions
8. 8. Case 4: Some ... All Statements: Some lizards are spock All spock are papers From the diagram it can be also concluded as Some lizards are papers
9. 9. Case 5: No Statement: No paper is scissor
10. 10. Case 5: No Statement: No paper is scissor