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Examine whether the statement pattern
[p → (~ q ˅ r)] ↔ ~[p → (q → r)] is a tautology, contradiction or contingency.
Concept: Statement Patterns and Logical Equivalence
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
Choose the correct alternative :
If p : He is intelligent.
q : He is strong
Then, symbolic form of statement “It is wrong that, he is intelligent or strong” is
Concept: Truth Value of Statement
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
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
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
The total cost of 3 T.V. and 2 V.C.R. is ₹ 35,000. The shopkeeper wants profit of ₹1000 per television and ₹ 500 per V.C.R. He can sell 2 T.V. and 1 V.C.R. and get the total revenue as ₹ 21,500. Find the cost price and the selling price of a T.V. and a V.C.R.
Concept: Application of Matrices
The sum of three numbers is 6. If we multiply third number by 3 and add it to the second number we get 11. By adding the first and third number we get a number which is double the second number. Use this information and find a system of linear equations. Find the three numbers using matrices.
Concept: Application of Matrices
Find matrices A and B, if `2"A" - "B" = [(6, -6, 0),(-4, 2, 1)] and "A" - 2"B" = [(3, 2, 8),(-2, 1, -7)]`
Concept: Algebra of Matrices
If A2 + 5A + 3I = 0, |A| ≠ 0, then A–1 = ______
Concept: Application of Matrices
State whether the following statement is True or False:
If `[(3, 0),(0, 2)][(x),(y)] = [(3),(2)]`, then x = 1 and y = – 1
Concept: Types of Matrices
