Mathematical Reasoning
Special Words/Phrases
- The compound statement with 'And' is true if all its component statements are true.
- The compound statement with 'And' is false if any of its component statements is false (this includes that case that some of its component statements are false or all its component statements are false).
- A compound statement with an 'Or' is true when one component statement is true or both the component statements are true.
- A compound statement with an 'Or' is false when both the component statements are false.
- The phrases "for all", "for some", "for no", "for every" and "there exists at least one" convey the idea of quantity and refer to some specific collection of number of objects. These phrases quantify the variables in open sentences. They are called quantifiers.
- The quantifier "for all" (or) "for every" are called the "universal quantifiers".
- The quantifiers "some" (or) "there exists at least one" are called "existential quantifiers"
- Dual of the statement : Two compound statement S1 and S2 are said to be dual to each other, if one can be obtained by the other by replacing ∧ by ∨ and ∨ by ∧ and t by c and c by t.
- Logically equivalence : Two statement S1 and S2 are said to be logically equivalence, if they have the same entries in the last column of the truth tables.
Eg:- p → q ⇒ ∼p ∨ q - In the switching circuits applications, the series combination is represented by ∧
- In the switching circuit application, the parallel combination is represented by ∨
Connectives and or
Exclusive and Inclusive or
Quantifiers
Disclaimer: Compete.etutor.co may from time to time provide links to third party Internet sites under their respective fair use policy and it may from time to time provide materials from such third parties on this website. These third party sites and any third party materials are provided for viewers convenience and for non-commercial educational purpose only. Compete does not operate or control in any respect any information, products or services available on these third party sites. Compete.etutor.co makes no representations whatsoever concerning the content of these sites and the fact that compete.etutor.co has provided a link to such sites is NOT an endorsement, authorization, sponsorship, or affiliation by compete.etutor.co with respect to such sites, its services, the products displayed, its owners, or its providers.
1. Truth table
| p | q | p ∧ q |
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
2.
| p | q | p ∨ q |
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |