HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

Using the rules in logic, write the negation of the following:

(p ∨ q) ∧ (q ∨ ∼r)

Using the rules in logic, write the negation of the following:

p ∧ (q ∨ r)

Using the rules in logic, write the negation of the following:

(p → q) ∧ r

Using the rules in logic, write the negation of the following:

(∼p ∧ q) ∨ (p ∧ ∼q)

Without using truth table prove that (p ∧ q) ∨ (∼ p ∧ q) v (p∧ ∼ q) ≡ p ∨ q

Without using truth table, prove that : [(p ∨ q) ∧ ∼p] →q is a tautology.

The simplified form of [(~ p v q) ∧ r] v [(p ∧ ~ q) ∧ r] is ______.

Without using truth table prove that

[(p ∧ q ∧ ∼ p) ∨ (∼ p ∧ q ∧ r) ∨ (p ∧ q ∧ r) ∨ (p ∧ ∼ q ∧ r) ≡ (p ∨ q) ∧ r

The statement p → (q → p) is equivalent to ______.

Show that the simplified form of (p ∧ q ∧ ∼ r) ∨ (r ∧ p ∧ q) ∨ (∼ p ∨ q) is q ∨ ∼ p.

Construct the switching circuit for the following statement : [p v (~ p ∧ q)] v [(- q ∧ r) v ~ p]

Construct the simplified circuit for the following circuit:

Find the symbolic form of the following switching circuit, construct its switching table and interpret it.

Construct the switching circuit for the statement (p ∧ q) ∨ (~ p) ∨ (p ∧ ~ q).

Simplify the following circuit so that the new circuit has minimum number of switches. Also, draw the simplified circuit.

Construct the new switching circuit for the following circuit with only one switch by simplifying the given circuit:

Find the symbolic form of the given switching circuit. Construct its switching table and interpret your result.

Express the following circuit in the symbolic form of logic and writ the input-output table.

Express the following circuit in the symbolic form of logic and write the input-output table.

Express the following circuit in the symbolic form of logic and write the input-output table.