Download App

Mathematical Logic (p-1) — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Mathematical Logic (p-1)1 Mark
Question
Without using truth table, show that : ~[(p ∧ q) → ~(q)] ≡ p ∧ q
✓

Answer

LHS = ~[(p ∧ q) → ~(~q)]
≡ (p ∧ q) ∧ ~(~q) ……(Negation of implication)
≡ (p ∧ q) ∧ q …..(Negation of negation)
≡ p ∧ (q ∧ q) …..(Associative Law)
≡ P ∧ q ……(Idempotent Law)
= RHS

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the following Question.(1 Marks)" from Mathematical Logic (p-1)→Mathematical Logic (p-1) — all question types→Maths (commerce) STD 12 Commerce / Arts question papers→Maharashtra Board STD 12 Commerce / Arts question papers→Maharashtra Board question paper generator→

Similar questions

Evalute : If $f^{\prime}(x)=\sqrt{x}$ and $f(1)=2$, then find the value of $f(x)$.
→
Find $\frac{d^2 y}{d x^2}$ if,
$
y=e^{\log x}
$
→
State which of the following sentences are statements in logic : How beautiful the flower is!
→
State which of the following sentences are statements in logic : Do not come inside the room.
→
Determine the order and degree of each of the following differential equations : $\sqrt{1+\frac{1}{\left(\frac{d y}{d x}\right)^2}}=\left(\frac{d y}{d x}\right)^{3 / 2}$
→
The rate of premium is 2% and other expenses are 0.075%. A cargo worth ₹ 3,50,100 is to be insured so that all its value and the cost of insurance will be recovered in the event of total loss.
→
Write the converse, inverse, and contrapositive of the following statement.

"If it snows, then they do not drive the car"

→
Evalute : $\int e^x\left[(\log x)^2+\frac{2 \log x}{x}\right] d x$
→
Find the area of the region bounded by the curve $x y=c^2$, the $X$-axis, and the lines $x=C_1 x=2 c$.
→
Write the following statements in symbolic form : Stock prices are high if and only if stocks are rising.
→