Digital-Logic-Design
October 15, 2023Binary-Trees
October 15, 2023Digital-Logic-Design
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Question 550
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If F and G are Boolean functions of degree n. Then, which of the following is true ?
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F ≤ F + G and F G ≤ F
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G ≤ F + G and F G ≥ G
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F ≥ F + G and F G ≤ F
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G ≥ F + G and F G ≤ F
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Question 550 Explanation:
Given data,
— F and G are boolean functions of degree n.
Step-1: Let n=4
Using n=22^n formula, we can find number of boolean functions
= 22^4
= 256
Stp-2: First consider F4→ F & G4→ G
F having 256 boolean functions and G having 256 boolean functions.
Option-A: F + G= 512 boolean functions and F*G= 14336 boolean functions.
F ≤ F + G and F G ≤ F FALSE because F G ≤ F is wrong
Option-B: G ≤ F + G and F G ≥ G TRUE
F + G= 512 boolean functions and F*G= 14336 boolean functions.
Option-C: F ≥ F + G and F G ≤ F FALSE because both are wrong
Option-D: G ≥ F + G and F G ≤ F FALSE because F G ≤ F is wrong.
— F and G are boolean functions of degree n.
Step-1: Let n=4
Using n=22^n formula, we can find number of boolean functions
= 22^4
= 256
Stp-2: First consider F4→ F & G4→ G
F having 256 boolean functions and G having 256 boolean functions.
Option-A: F + G= 512 boolean functions and F*G= 14336 boolean functions.
F ≤ F + G and F G ≤ F FALSE because F G ≤ F is wrong
Option-B: G ≤ F + G and F G ≥ G TRUE
F + G= 512 boolean functions and F*G= 14336 boolean functions.
Option-C: F ≥ F + G and F G ≤ F FALSE because both are wrong
Option-D: G ≥ F + G and F G ≤ F FALSE because F G ≤ F is wrong.
Correct Answer: B
Question 550 Explanation:
Given data,
— F and G are boolean functions of degree n.
Step-1: Let n=4
Using n=22^n formula, we can find number of boolean functions
= 22^4
= 256
Stp-2: First consider F4→ F & G4→ G
F having 256 boolean functions and G having 256 boolean functions.
Option-A: F + G= 512 boolean functions and F*G= 14336 boolean functions.
F ≤ F + G and F G ≤ F FALSE because F G ≤ F is wrong
Option-B: G ≤ F + G and F G ≥ G TRUE
F + G= 512 boolean functions and F*G= 14336 boolean functions.
Option-C: F ≥ F + G and F G ≤ F FALSE because both are wrong
Option-D: G ≥ F + G and F G ≤ F FALSE because F G ≤ F is wrong.
— F and G are boolean functions of degree n.
Step-1: Let n=4
Using n=22^n formula, we can find number of boolean functions
= 22^4
= 256
Stp-2: First consider F4→ F & G4→ G
F having 256 boolean functions and G having 256 boolean functions.
Option-A: F + G= 512 boolean functions and F*G= 14336 boolean functions.
F ≤ F + G and F G ≤ F FALSE because F G ≤ F is wrong
Option-B: G ≤ F + G and F G ≥ G TRUE
F + G= 512 boolean functions and F*G= 14336 boolean functions.
Option-C: F ≥ F + G and F G ≤ F FALSE because both are wrong
Option-D: G ≥ F + G and F G ≤ F FALSE because F G ≤ F is wrong.
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