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The contrapositive statement of the proposition p → ~ q is

1) ~ p → q 2) ~ q → p 3) q → ~ p 4) None of these Solution: (3) q → ~ p The given conditional statement is, p → ~ q The... View Article

Which of the following is not a logical statement?

1) 8 is less than 6 2) Every set is a finite set 3) Kashmir is far from here 4) The Sun is a star Solution: (3) Kashmir is far from... View Article

If p : “roses are red” and q : “the sun is a star”. Then, the verbal translation of (~ p) ∨ q is

1) roses are not red and the Sun is not a star 2) it is not true that roses are red or the Sun is not a star 3) it is not true that roses... View Article

The negation of p → (~ p ∨ q) is

1) p ∨ (p ∨ ~ q) 2) p → ~ (p ∨ q) 3) p → q 4) p ∧ ~ q Solution: (4) p ∧ ~ q p q ~ p ~ q (~ p ∨ q) p → (~ p ∨ q) (~ p ∨... View Article

The only statement among the following which is a tautology, is

1) B → [A ∧ (A → B)] 2) A ∧ (A ∨ B) 3) A ∨ (A ∧ B) 4) [A ∧ (A → B) → B] Solution: (4) [A ∧ (A → B) → B] A ∨ (A ∨ B) = A and A ∧... View Article

Consider the following statements. p: Suman is brilliant. q: Suman is rich. r: Suman is honest. The negation of the statement “Suman is brilliant and dishonest if and only if Suman is rich” can be expressed as

p: Suman is brilliant. q: Suman is rich. r: Suman is honest. The negation of the statement “Suman is brilliant and dishonest if and only if... View Article

The negative of the compound proposition p ∨ (~ p ∨ q) is

(1) (p ∧ ~ q) ∨ ~ p (2) (p ∧ ~ q) ∧ ~ p (3) (p ∧ ~ q) ∨ ~ p (4) None of the above Solution: (2) (p ∧ ~ q) ∧ ~ p... View Article

Consider the following statements: Statement I: (p ∧ ~ q) ∧ (~ p ∧ q) is a fallacy. Statement II: (p → q) ↔ (~ q → ~ p) is a tautology.

Statement I: (p ∧ ~ q) ∧ (~ p ∧ q) is a fallacy Statement II: (p → q) ↔ (~ q → ~ p) is a tautology. 1) Statement I is correct, Statement II is... View Article

The truth values of p, q and r for which (p ∧ q) ∨ (~ r) has truth value F are respectively

1) F, T, F 2) F, F, F 3) T, T, T 4) T, F, F 5) F, F, T Solution: (5) F, F, T Hence, (p ∧ q) ∨ (~ r) has truth value F when... View Article

If p, q and r are any three logical statements, then which one of the following is correct?

1) ~ [p ∧ (~ q)] ≡ (~ p) ∧ q 2) ~ (p ∨ q) ∧ (~ r) ≡ (~ p) ∨ (~ q) ∨ (~ r) 3) ~ [p ∨ (~ q)] ≡ (~ p) ∧ q 4) ~ [p ∧ (~ q)] ≡ (~ p) ∧ ~ q... View Article

Which of the following is not a correct statement?

1) Mathematics is interesting 2) √3 is a prime number 3) √2 is an irrational number 4) The sun is a star Solution: (2) √3 is a prime... View Article

The statement (p ⇒ q) ⇔ (~ p ∧ q) is a

1) tautology 2) contradiction 3) Neither (a) nor (b) 4) None of these Solution: (3) Neither (a) nor (b) p q ~... View Article

The negation of p → (q ∧ r)

1) ~ p → ~ (q ∨ r) 2) ~ p → ~ (q ∧ r) 3) (q ∧ r) → p 4) p ∧ (~ q ∨ ~ r) Solution: (4) p ∧ (~ q ∨ ~ r) ~ (p ∨ q) ≅ p ∧ ~ q ~ (p ∨... View Article

The Statement ~ (p ↔ ~ q) is

1) equivalent to p ↔ q 2) equivalent to ~ p ↔ q 3) a tautology 4) a fallacy Solution: (1) equivalent to p ↔ q... View Article

A solid reflects incident light and its electrical conductivity decreases with temperature. The binding in this solids

(a) Ionic(b) Covalent(c) Metallic(d) Molecular Solution: (c) MetallicMetals reflects incident light by the vibrations of free electrons under... View Article

In an n-type semiconductor, the donor energy level lies

(a) at the center of the energy gap (b) just below the conduction band (c) just above the valence band (d) in the conduction bandSolution: (b)... View Article

When a solid with a band gap has a donor level just below its empty energy band, the solid is

(a) a condutor(b) a insulator(c) an n-type semiconductor(d) a p-type semiconductor Solution:(c) an n-type semiconductorIn an n-type... View Article

For an insulator, the forbidden energy gap is

(a) 1 MeV(b) 0.1 MeV(c) 1 eV(d) 5 eV Solution: (d) 5 eVForbidden energy gap, also known as band gap refers to the energy difference (eV) between... View Article

The energy band gap (distance between the conduction band and valence band) in conductor is

(a) 0(b) 4 angstrom(c) 10 angstrom(d) 100 angstrom Solution: (a) 0In conductors, the valence band and conduction band overlap each other or have... View Article

In the bandgap between valence hand and conduction band in a material is 5.0 eV, then the material is

a) insulatorb) semiconductorc) good conductord) superconductor Solution: a) insulatorGenerally, Insulators have very large band gap and thus... View Article

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