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Write the following compound statements symbolically.
Triangle is equilateral or isosceles
Concept: Logical Connective, Simple and Compound Statements
If statements p, q are true and r, s are false, determine the truth values of the following.
(p ∧ ~r) ∧ (~q ∨ s)
Concept: Truth Value of Statement
Without using truth table prove that:
~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Concept: Logical Connective, Simple and Compound Statements
Write the following statement in symbolic form:
Milk is white if and only if the sky is not blue.
Concept: Logical Connective, Simple and Compound Statements
Write the following statements in symbolic form
If Kutab – Minar is in Delhi then Taj - Mahal is in Agra
Concept: Logical Connective, Simple and Compound Statements
Write the following statements in symbolic form
Even though it is not cloudy, it is still raining
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: Tautology, Contradiction, and Contingency
Use quantifiers to convert the given open sentence defined on N into a true statement
3x – 4 < 9
Concept: Quantifier and Quantified Statements in Logic
Use quantifiers to convert the given open sentence defined on N into a true statement
Y + 4 > 6
Concept: Quantifier and Quantified Statements in Logic
The negation of p ^ (q → r) is ______.
Concept: Negations of Compound Statements
Using truth table verify that:
(p ∧ q)∨ ∼ q ≡ p∨ ∼ q
Concept: Statement Patterns and Logical Equivalence
Without using truth table prove that (p ∧ q) ∨ (∼ p ∧ q) v (p∧ ∼ q) ≡ p ∨ q
Concept: Algebra of Statements
Simplify the given circuit by writing its logical expression. Also, write your conclusion.
Concept: Application of Logic to Switching Circuits
Construct the truth table for the statement pattern:
[(p → q) ∧ q] → p
Concept: Logical Connective, Simple and Compound Statements
The dual of statement t ∨ (p ∨ q) is ______.
Concept: Duality
Apply the given elementary transformation of the following matrix.
A = `[(1,0),(-1,3)]`, R1↔ R2
Concept: Elementry Transformations
If A = `[("x",0,0),(0,"y",0),(0,0,"z")]` is a non-singular matrix, then find A−1 by using elementary row transformations. Hence, find the inverse of `[(2,0,0),(0,1,0),(0,0,-1)]`
Concept: Elementry Transformations
Find the inverse of A = `[("cos" theta, -"sin" theta, 0),("sin" theta, "cos" theta, 0),(0,0,1)]` by elementary row transformations.
Concept: Elementry Transformations
Express the following equations in matrix form and solve them by the method of reduction:
x − y + z = 1, 2x − y = 1, 3x + 3y − 4z = 2
Concept: Application of Matrices
The value of x, y, z for the following system of equations x + y + z = 6, x − y+ 2z = 5, 2x + y − z = 1 are ______
Concept: Applications of Determinants and Matrices
