DigitalLogicDesign
October 15, 2023BinaryTrees
October 15, 2023DigitalLogicDesign
Question 550

If F and G are Boolean functions of degree n. Then, which of the following is true ?
F ≤ F + G and F G ≤ F


G ≤ F + G and F G ≥ G


F ≥ F + G and F G ≤ F


G ≥ F + G and F G ≤ F

Question 550 Explanation:
Given data,
— F and G are boolean functions of degree n.
Step1: Let n=4
Using n=2^{2^n} formula, we can find number of boolean functions
= 2^{2^4}
= 256
Stp2: First consider F^{4}→ F & G^{4}→ G
F having 256 boolean functions and G having 256 boolean functions.
OptionA: 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
OptionB: G ≤ F + G and F G ≥ G TRUE
F + G= 512 boolean functions and F*G= 14336 boolean functions.
OptionC: F ≥ F + G and F G ≤ F FALSE because both are wrong
OptionD: G ≥ F + G and F G ≤ F FALSE because F G ≤ F is wrong.
— F and G are boolean functions of degree n.
Step1: Let n=4
Using n=2^{2^n} formula, we can find number of boolean functions
= 2^{2^4}
= 256
Stp2: First consider F^{4}→ F & G^{4}→ G
F having 256 boolean functions and G having 256 boolean functions.
OptionA: 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
OptionB: G ≤ F + G and F G ≥ G TRUE
F + G= 512 boolean functions and F*G= 14336 boolean functions.
OptionC: F ≥ F + G and F G ≤ F FALSE because both are wrong
OptionD: 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.
Step1: Let n=4
Using n=2^{2^n} formula, we can find number of boolean functions
= 2^{2^4}
= 256
Stp2: First consider F^{4}→ F & G^{4}→ G
F having 256 boolean functions and G having 256 boolean functions.
OptionA: 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
OptionB: G ≤ F + G and F G ≥ G TRUE
F + G= 512 boolean functions and F*G= 14336 boolean functions.
OptionC: F ≥ F + G and F G ≤ F FALSE because both are wrong
OptionD: G ≥ F + G and F G ≤ F FALSE because F G ≤ F is wrong.
— F and G are boolean functions of degree n.
Step1: Let n=4
Using n=2^{2^n} formula, we can find number of boolean functions
= 2^{2^4}
= 256
Stp2: First consider F^{4}→ F & G^{4}→ G
F having 256 boolean functions and G having 256 boolean functions.
OptionA: 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
OptionB: G ≤ F + G and F G ≥ G TRUE
F + G= 512 boolean functions and F*G= 14336 boolean functions.
OptionC: F ≥ F + G and F G ≤ F FALSE because both are wrong
OptionD: G ≥ F + G and F G ≤ F FALSE because F G ≤ F is wrong.
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