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Exam: Maharashtra HSC Class 12
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Set · 7 questions
Construct the truth table for each of the following statement patterns.
Q2226
#2226
Mathematics → Mathematical Logic → Truth Tables of Compound Statements
·
Easy
Add
(
p
∧
q
)
↔
(
q
∨
r
)
(p \wedge q) \leftrightarrow (q \vee r)
(
p
∧
q
)
↔
(
q
∨
r
)
Show model answer
[Q1.2 Ex 1.2 Q.1 (iii) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Q2227
#2227
Mathematics → Mathematical Logic → Truth Tables of Compound Statements
·
Easy
Add
p
→
[
∼
(
q
∧
r
)
]
p \to [\sim (q \wedge r)]
p
→
[
∼
(
q
∧
r
)]
Show model answer
[Q1.2 Ex 1.2 Q.1 (iv) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
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Q2228
#2228
Mathematics → Mathematical Logic → Truth Tables of Compound Statements
·
Easy
Add
∼
p
∧
[
(
p
∨
∼
q
)
∧
q
]
\sim p \wedge [(p \vee \sim q) \wedge q]
∼
p
∧
[(
p
∨
∼
q
)
∧
q
]
Show model answer
[Q1.2 Ex 1.2 Q.1 (v) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Q2229
#2229
Mathematics → Mathematical Logic → Truth Tables of Compound Statements
·
Easy
Add
(
∼
p
→
∼
q
)
∧
(
∼
q
→
∼
p
)
(\sim p \to \sim q) \wedge (\sim q \to \sim p)
(
∼
p
→∼
q
)
∧
(
∼
q
→∼
p
)
Show model answer
[Q1.2 Ex 1.2 Q.1 (vi) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Q2230
#2230
Mathematics → Mathematical Logic → Truth Tables of Compound Statements
·
Easy
Add
(
q
→
p
)
∨
(
∼
p
↔
q
)
(q \to p) \vee (\sim p \leftrightarrow q)
(
q
→
p
)
∨
(
∼
p
↔
q
)
Show model answer
[Q1.2 Ex 1.2 Q.1 (vii) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Q2231
#2231
Mathematics → Mathematical Logic → Truth Tables of Compound Statements
·
Moderate
Add
[
p
→
(
q
→
r
)
]
↔
[
(
p
∧
q
)
→
r
]
[p \to (q \to r)] \leftrightarrow [(p \wedge q) \to r]
[
p
→
(
q
→
r
)]
↔
[(
p
∧
q
)
→
r
]
Show model answer
[Q1.2 Ex 1.2 Q.1 (viii) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Q2232
#2232
Mathematics → Mathematical Logic → Truth Tables of Compound Statements
·
Easy
Add
(
p
∨
∼
q
)
→
(
r
∧
p
)
(p \vee \sim q) \to (r \wedge p)
(
p
∨
∼
q
)
→
(
r
∧
p
)
Show model answer
[Q1.2 Ex 1.2 Q.1 (x) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Set · 9 questions
Using truth tables prove the following logical equivalences.
Q2233
#2233
Mathematics → Mathematical Logic → Logical Equivalence and Algebra of Statements
·
Easy
Add
∼
p
∧
q
≡
(
p
∨
q
)
∧
∼
p
\sim p \wedge q \equiv (p \vee q) \wedge \sim p
∼
p
∧
q
≡
(
p
∨
q
)
∧
∼
p
Show model answer
[Q1.2 Ex 1.2 Q.2 (i) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Q2234
#2234
Mathematics → Mathematical Logic → Logical Equivalence and Algebra of Statements
·
Moderate
Add
∼
(
p
∨
q
)
∨
(
∼
p
∧
q
)
≡
∼
p
\sim (p \vee q) \vee (\sim p \wedge q) \equiv \sim p
∼
(
p
∨
q
)
∨
(
∼
p
∧
q
)
≡∼
p
Show model answer
[Q1.2 Ex 1.2 Q.2 (ii) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Q2235
#2235
Mathematics → Mathematical Logic → Logical Equivalence and Algebra of Statements
·
Moderate
Add
p
↔
q
≡
∼
[
(
p
∨
q
)
∧
∼
(
p
∧
q
)
]
p \leftrightarrow q \equiv \sim [(p \vee q) \wedge \sim (p \wedge q)]
p
↔
q
≡∼
[(
p
∨
q
)
∧
∼
(
p
∧
q
)]
Show model answer
[Q1.2 Ex 1.2 Q.2 (iii) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Q2236
#2236
Mathematics → Mathematical Logic → Logical Equivalence and Algebra of Statements
·
Moderate
Add
p
→
(
q
→
p
)
≡
∼
p
→
(
p
→
q
)
p \to (q \to p) \equiv \sim p \to (p \to q)
p
→
(
q
→
p
)
≡∼
p
→
(
p
→
q
)
Show model answer
[Q1.2 Ex 1.2 Q.2 (iv) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Q2237
#2237
Mathematics → Mathematical Logic → Logical Equivalence and Algebra of Statements
·
Moderate
Add
(
p
∨
q
)
→
r
≡
(
p
→
r
)
∧
(
q
→
r
)
(p \vee q) \to r \equiv (p \to r) \wedge (q \to r)
(
p
∨
q
)
→
r
≡
(
p
→
r
)
∧
(
q
→
r
)
Show model answer
[Q1.2 Ex 1.2 Q.2 (v) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Q2238
#2238
Mathematics → Mathematical Logic → Logical Equivalence and Algebra of Statements
·
Moderate
Add
p
→
(
q
∧
r
)
≡
(
p
→
q
)
∧
(
p
→
r
)
p \to (q \wedge r) \equiv (p \to q) \wedge (p \to r)
p
→
(
q
∧
r
)
≡
(
p
→
q
)
∧
(
p
→
r
)
Show model answer
[Q1.2 Ex 1.2 Q.2 (vi) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Q2239
#2239
Mathematics → Mathematical Logic → Logical Equivalence and Algebra of Statements
·
Moderate
Add
p
∧
(
q
∨
r
)
≡
(
p
∧
q
)
∨
(
p
∧
r
)
p \wedge (q \vee r) \equiv (p \wedge q) \vee (p \wedge r)
p
∧
(
q
∨
r
)
≡
(
p
∧
q
)
∨
(
p
∧
r
)
Show model answer
[Q1.2 Ex 1.2 Q.2 (vii) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Q2240
#2240
Mathematics → Mathematical Logic → Logical Equivalence and Algebra of Statements
·
Moderate
Add
[
∼
(
p
∨
q
)
∨
(
p
∨
q
)
]
∧
r
≡
r
[\sim (p \vee q) \vee (p \vee q)] \wedge r \equiv r
[
∼
(
p
∨
q
)
∨
(
p
∨
q
)]
∧
r
≡
r
Show model answer
[Q1.2 Ex 1.2 Q.2 (viii) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Q2241
#2241
Mathematics → Mathematical Logic → Logical Equivalence and Algebra of Statements
·
Moderate
Add
∼
(
p
↔
q
)
≡
(
p
∧
∼
q
)
∨
(
q
∧
∼
p
)
\sim (p \leftrightarrow q) \equiv (p \wedge \sim q) \vee (q \wedge \sim p)
∼
(
p
↔
q
)
≡
(
p
∧
∼
q
)
∨
(
q
∧
∼
p
)
Show model answer
[Q1.2 Ex 1.2 Q.2 (ix) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Set · 9 questions
Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.
Q2242
#2242
Mathematics → Mathematical Logic → Tautology, Contradiction and Contingency
·
Easy
Add
(
p
∧
q
)
→
(
q
∨
p
)
(p \wedge q) \to (q \vee p)
(
p
∧
q
)
→
(
q
∨
p
)
Show model answer
[Q1.2 Ex 1.2 Q.3 (i) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Q2243
#2243
Mathematics → Mathematical Logic → Tautology, Contradiction and Contingency
·
Easy
Add
(
p
→
q
)
↔
(
∼
p
∨
q
)
(p \to q) \leftrightarrow (\sim p \vee q)
(
p
→
q
)
↔
(
∼
p
∨
q
)
Show model answer
[Q1.2 Ex 1.2 Q.3 (ii) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Q2244
#2244
Mathematics → Mathematical Logic → Tautology, Contradiction and Contingency
·
Easy
Add
[
∼
(
∼
p
∧
∼
q
)
]
∨
q
[\sim (\sim p \wedge \sim q)] \vee q
[
∼
(
∼
p
∧
∼
q
)]
∨
q
Show model answer
[Q1.2 Ex 1.2 Q.3 (iii) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Q2245
#2245
Mathematics → Mathematical Logic → Tautology, Contradiction and Contingency
·
Easy
Add
[
(
p
→
q
)
∧
q
]
→
p
[(p \to q) \wedge q] \to p
[(
p
→
q
)
∧
q
]
→
p
Show model answer
[Q1.2 Ex 1.2 Q.3 (iv) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Q2246
#2246
Mathematics → Mathematical Logic → Tautology, Contradiction and Contingency
·
Easy
Add
[
(
p
→
q
)
∧
∼
q
]
→
∼
p
[(p \to q) \wedge \sim q] \to \sim p
[(
p
→
q
)
∧
∼
q
]
→∼
p
Show model answer
[Q1.2 Ex 1.2 Q.3 (v) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Q2247
#2247
Mathematics → Mathematical Logic → Tautology, Contradiction and Contingency
·
Easy
Add
(
p
↔
q
)
∧
(
p
→
∼
q
)
(p \leftrightarrow q) \wedge (p \to \sim q)
(
p
↔
q
)
∧
(
p
→∼
q
)
Show model answer
[Q1.2 Ex 1.2 Q.3 (vi) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Q2248
#2248
Mathematics → Mathematical Logic → Tautology, Contradiction and Contingency
·
Easy
Add
∼
(
∼
q
∧
p
)
∧
q
\sim (\sim q \wedge p) \wedge q
∼
(
∼
q
∧
p
)
∧
q
Show model answer
[Q1.2 Ex 1.2 Q.3 (vii) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Q2249
#2249
Mathematics → Mathematical Logic → Tautology, Contradiction and Contingency
·
Easy
Add
(
p
∧
∼
q
)
↔
(
p
→
q
)
(p \wedge \sim q) \leftrightarrow (p \to q)
(
p
∧
∼
q
)
↔
(
p
→
q
)
Show model answer
[Q1.2 Ex 1.2 Q.3 (viii) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
Q2250
#2250
Mathematics → Mathematical Logic → Tautology, Contradiction and Contingency
·
Easy
Add
(
∼
p
→
q
)
∧
(
p
∧
r
)
(\sim p \to q) \wedge (p \wedge r)
(
∼
p
→
q
)
∧
(
p
∧
r
)
Show model answer
[Q1.2 Ex 1.2 Q.3 (ix) · Maharashtra State Board (Class 12) — Mathematical Logic (Balbharati textbook)]
Report
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