HSC Science (Computer Science) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

If `bar("c") = 3bar("a") - 2bar("b")` then prove that `[(bar("a"), bar("b"), bar("c"))]` = 0

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

`"Check whether the vectors"  2hati+2hatj+3hatk,-3hati+3hatj+2hatk  "and"  3hati+4hatk  "form a triangle or not".`

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.

In the triangle `PQR, bar (PQ) = 2bara and bar (QR) = 2barb`. The mid-point of PR is M. Find following vectors in terms of `bar a and bar b`.

1. `bar(PR)`
2. `bar(PM)`
3. `bar(QM)`

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.