###### Digital-Logic-Design

October 15, 2023###### Binary-Trees

October 15, 2023# Digital-Logic-Design

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.

Step-1: Let n=4

Using n=2

= 2

= 256

Stp-2: First consider F

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=2

^{2^n}formula, we can find number of boolean functions= 2

^{2^4}= 256

Stp-2: First consider F

^{4}→ F & G^{4}→ GF 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=2

= 2

= 256

Stp-2: First consider F

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=2

^{2^n}formula, we can find number of boolean functions= 2

^{2^4}= 256

Stp-2: First consider F

^{4}→ F & G^{4}→ GF 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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