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Consider the following statements.
- If D is dog, then D is very good.
- If D is very good, then D is dog.
- If D is not very good, then D is not a dog.
- If D is not a dog, then D is not very good.
Identify the pairs of statements having the same meaning. Justify.
Concept: Logical Connective, Simple and Compound Statements
Choose the correct alternative:
Negation of p → (p ˅ ~q) is
Concept: Logical Connective, Simple and Compound Statements
The dual of the statement (p ˅ q) ˄ (r ˅ s) is ______.
Concept: Truth Value of Statement
Negation of “Some men are animal” is ______.
Concept: Logical Connective, Simple and Compound Statements
Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”
Concept: Logical Connective, Simple and Compound Statements
Using truth table prove that ~ p ˄ q ≡ ( p ˅ q) ˄ ~ p
Concept: Truth Value of Statement
Examine whether the statement pattern
[p → (~ q ˅ r)] ↔ ~[p → (q → r)] is a tautology, contradiction or contingency.
Concept: Statement Patterns and Logical Equivalence
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r).
Concept: Truth Value of Statement
Complete the truth table.
| p | q | r | q → r | r → p | (q → r) ˅ (r → p) |
| T | T | T | T | `square` | T |
| T | T | F | F | `square` | `square` |
| T | F | T | T | `square` | T |
| T | F | F | T | `square` | `square` |
| F | T | T | `square` | F | T |
| F | T | F | `square` | T | `square` |
| F | F | T | `square` | F | T |
| F | F | F | `square` | T | `square` |
The given statement pattern is a `square`
Concept: Statement Patterns and Logical Equivalence
If p ∨ q is true, then the truth value of ∼ p ∧ ∼ q is ______.
Concept: Algebra of Statements
Write the converse, inverse, and contrapositive of the statement. "If 2 + 5 = 10, then 4 + 10 = 20."
Concept: Logical Connective, Simple and Compound Statements
Determine whether the following statement pattern is a tautology, contradiction, or contingency:
[(∼ p ∧ q) ∧ (q ∧ r)] ∧ (∼ q)
Concept: Statement Patterns and Logical Equivalence
Draw Venn diagram for the following:
No policeman is thief
Concept: Venn Diagrams
Draw Venn diagram for the following:
Some doctors are rich
Concept: Venn Diagrams
Draw Venn diagram for the following:
Some students are not scholars
Concept: Venn Diagrams
Conditional of p → q is equivalent to p → ∼ q.
Concept: Logical Connective, Simple and Compound Statements
Converse of the statement q `rightarrow` p is ______.
Concept: Logical Connective, Simple and Compound Statements
Write the negation of the following statement:
(p `rightarrow` q) ∨ (p `rightarrow` r)
Concept: Statement Patterns and Logical Equivalence
The converse of contrapositive of ∼p → q is ______.
Concept: Statement Patterns and Logical Equivalence
If x = a sin t and `y = a (cost+logtan(t/2))` ,find `((d^2y)/(dx^2))`
Concept: Second Order Derivative
