Download App

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

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Mathematical Logic (p-1)5 Marks
Question
Assuming the first statement as p and second as q, write the following statements in symbolic form:
(i) $x^3 + y^3 = (x + y)^3$^, iff $xy = 0.$
(ii) The drug is effective though it has side effects.
(iii) If a real number is not rational, then it must be irrational.
(iv) It is not true that Ram is tall and handsome.
(v) Even though it is not cloudy, it is still raining.
(vi) It is not true that intelligent persons are neither polite nor helpful.
(vii) If the question paper is not easy, then we shall not pass.
✓

Answer

1. Let p : $x^3 + y^3 = (x + y)^3.$
$q : xy = 0.$
Then the symbolic form of the given statement is p ↔ q.
2. Let p : The drug is effective.
q : It has side effects.
Then the symbolic form of the given statement is p ∧ q.
3. Let p : A real number is not rational.
q : It must be irrational.
Then the symbolic form of the given statement is p → q.
4. Let p : Ram is tall.
q : Ram is handsome.
Then the symbolic form of the given statement is ~(p ∧ q).
5. The given statement is equivalent to:
It is not cloudy and it is still raining,
Let p : It is not cloudy.
q : It is still raining.
Then the symbolic form of the given statement is p ∧ q.
6. Let p : Intelligent persons are neither polite nor helpful.
Then the symbolic form of the given statement is ~p.
7. Let p : The question paper is not easy.
q : We shall not pass.
Then the symbolic form of the given statement is p → q.

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.(5 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

Find the equations of tangent and normal to the following curves: $y=x^2+4 x$ at the point whose ordinate is -3 .
→
If $x ^7 \cdot y ^9=( x + y )^{16}$, then show that $\frac{d y}{d x}=\frac{y}{x}$.
→
the following table shows the wheat yield (‘000 tonnes) in India for the years 1959 to 1968.
YEARYIELDYEARYIELD
1959019640
1960119654
1961219661
1962319672
19631196810
Fit a trend line to the above data by the method of least squares.
→
Find inverse of the following matrices (if they exist) by elementary transformation : $\left[\begin{array}{ccc}2 & -3 & 3 \\ 2 & 2 & 3 \\ 3 & -2 & 2\end{array}\right]$
→
Minimize z = 7x + y Subject to 5x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0
→
If $a x^2+2 h x y+b y^2=0$, then show that $\frac{d^2 y}{d x^2}=0$.
→
A bill of $\text{₹} 51,000$ was drawn on $18$th February $2010$ for $9$ months. It was encashed on $28$th June $2010$ at $5\%$ p.a. Calculate the banker’s gain and true discount.
→
The sum of three numbers is $6$. If we multiply the third number by $3$ and add it to the second number, we get $11$. By adding first and third numbers we get a number that is double the second number. Use this information and find a system of linear equations. Find the three numbers using matrices.
→
Maximize z = 6x + 10y, subject to 3x + 5y ≤ 10, 5x + 3y ≤ 15, x ≥ 0, y ≥ 0
→
Assuming the first statement as p and second as q, write the following statements in symbolic form:
(i) The Sun has set and Moon has risen.
(ii) Mona likes Mathematics and Physics.
(iii) 3 is a prime number if 3 is a perfect square number.
(iv) Kavita is brilliant and brave.
(v) If Kiran drives a car, then Sameer will walk.
(vi) The necessary condition for the existence of a tangent to the curve of the function is continuity.
(vii) To be brave is necessary and sufficient condition to climb Mount Everest.
→