Vidaara.orgClass 11 · Mathematics
CodeVID-M11-16-MR-01
Statements & Logical Connectives — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
Which is a statement?
- A.Open the gate.
- B.$7$ is an even number.
- C.What time is it?
- D.Hurrah!
2.
The negation of $p$ has truth value:
- A.same as $p$
- B.opposite to $p$
- C.always true
- D.always false
3.
$p \wedge q$ is false when:
- A.both true
- B.at least one false
- C.both false only
- D.never
4.
The default mathematical "or" is:
- A.exclusive
- B.inclusive
- C.neither
- D.undefined
5.
A sentence with a free variable $x$ is:
- A.a true statement
- B.a false statement
- C.an open sentence, not a statement
- D.a command
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Is "Please switch off the light" a statement? Why?
7.
Write the negation of "$\sqrt{3}$ is irrational".
8.
Identify the connective in "$5$ is odd and $5$ is prime".
9.
State the truth value of "$2 > 3$ or $4 > 1$".
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Classify as statement / not a statement: (a) "$x + 2 = 7$", (b) "All squares are rectangles", (c) "Is $0$ even?".
11.
Break "$36$ is divisible by $4$ and by $9$" into components and give its truth value.
12.
Is the "or" in "A number is positive or negative" inclusive or exclusive?
13.
Write $p \wedge q$ and $p \vee q$ for $p$: "It is sunny", $q$: "It is windy".
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Construct the truth table for $\sim p$, $p \wedge q$ and $p \vee q$ for all four combinations of $p,q$.
15.
For each, state whether it is a statement and (if so) its truth value: (a) "The product of two negative numbers is positive", (b) "Give me a glass of water", (c) "$11$ is a composite number", (d) "$x^2 \ge 0$ for all real $x$".
Answer Key
Section A — Multiple Choice Questions
- (B) $7$ is an even number.
- (B) opposite to $p$
- (B) at least one false
- (B) inclusive
- (C) an open sentence, not a statement
Section B — Short Answer (2 marks)
- No — it is a request/command with no truth value.
- "$\sqrt{3}$ is not irrational" (i.e. it is rational).
- "And" ($\wedge$); both components are true so the statement is true.
- True — the second component is true (inclusive or).
Section C — Short Answer (3 marks)
- (a) not a statement (open sentence); (b) statement (true); (c) not a statement (question).
- $p$: "$36$ is divisible by $4$" (true), $q$: "$36$ is divisible by $9$" (true); $p \wedge q$ is true.
- Exclusive — a non-zero number cannot be both at once.
- $p \wedge q$: "It is sunny and windy"; $p \vee q$: "It is sunny or windy".
Section D — Long Answer (5 marks)
- For (T,T): $\sim p$=F, $p\wedge q$=T, $p\vee q$=T. (T,F): F, F, T. (F,T): T, F, T. (F,F): T, F, F.
- (a) statement, true; (b) not a statement (command); (c) statement, false; (d) statement, true.
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