Question
Using the truth table, prove the following logical equivalences:
~p ∧ q ≡ (p ∨ q) ∧ ~p
~p ∧ q ≡ (p ∨ q) ∧ ~p
✓
Answer
~p ∧ q ≡ (p ∨ q) ∧ ~p
The entries in columns 4 and 6 are identical.
∴ ~p ∧ q ≡ (p ∨ q) ∧ ~p
The entries in columns 4 and 6 are identical.
∴ ~p ∧ q ≡ (p ∨ q) ∧ ~p
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Evalute : $\int \sqrt{x^2+2 x+5} d x$
→A car firm has $2$ cars, which are hired out day by day. The number of cars hired on a day follows a Poisson distribution with a mean of $1.5.$ Find the probability that
(i) no car is used on a given day.
(ii) some demand is refused on a given day, given $e^{-1.5} = 0.2231.$
→(i) no car is used on a given day.
(ii) some demand is refused on a given day, given $e^{-1.5} = 0.2231.$
f p : He swims.
q : Water is warm.
Give the verbal statements for the following symbolic statements:
(i) p ↔ ~q
(ii) ~(p ∨ q)
(iii) q → p
(iv) q ∧ ~p
q : Water is warm.
Give the verbal statements for the following symbolic statements:
(i) p ↔ ~q
(ii) ~(p ∨ q)
(iii) q → p
(iv) q ∧ ~p
Find the Price Index Number using the Simple Aggregate Method.
Use 1995 as the base year in the following problem.
Use 1995 as the base year in the following problem.
| COMMODITY | P | Q | R | S | T |
| PRICE ( IN RS. ) IN 1995 | 15 | 20 | 24 | 23 | 28 |
| PRICE (IN RS.) IN 2000 | 27 | 38 | 32 | 40 | 45 |
Evaluate the following integrals : $\int_0^1 x(1-x)^5 d x$
→Find the present value of an annuity immediate of $\text{₹} 36,000$ p.a. for 3 years at $9 \%$ p.a. compounded annually. [Given: $\left.(1.09)^{-3}=0.7722\right]$
→Using the truth table, prove the following logical equivalences:
p ∧ (~p ∨ q) ≡ p ∧ q
p ∧ (~p ∨ q) ≡ p ∧ q
Prepare the truth tables for the following statement patterns : p → (~p ∨ q)
Prepare the truth tables for the following statement patterns : (~p ∨ q) ∧ (~p ∨ ~q)
Check whether following matrices are invertible or not: $\left[\begin{array}{lll}3 & 4 & 3 \\ 1 & 1 & 0 \\ 1 & 4 & 5\end{array}\right]$
→