Answer to Question #349693 in Discrete Mathematics for pjreston

Question

1.      Evaluate each of these expressions.

a)  1 1000 ∧ (0 1011 ∨ 1 1011)

b) (0 1111 ∧ 1 0101) ∨ 0 1000

c)  (0 1010 ⊕ 1 1011) ⊕ 0 1000

d) (1 1011 ∨ 0 1010) ∧ (1 0001 ∨ 1 1011) 

Answer 1

$∧$ is a logical "and": $1∧1=1,\: 1∧0=0,\: 0∧1=0,\: 0∧0=0.$

$∨$ is a logical "or": $1∨1=1, \:1∨0=1,\: 0∨1=1, \:0∨0=0.$

$⊕$ is a logical "xor": $1⊕1=0,\: 1⊕0=1,\: 0⊕1=1,\: 0⊕0=0.$

So we have:

a)  $1 1000 ∧ (0 1011 ∨ 1 1011)=11000\land$ 11011=11000

b) $(0 1111 ∧ 1 0101) ∨ 0 1000=00101 ∨ 0 1000=01101$

c)  $(0 1010 ⊕ 1 1011) ⊕ 0 1000=10001⊕ 0 1000=11001$

d) $(1 1011 ∨ 0 1010) ∧ (1 0001 ∨ 1 1011) =11011∧11011=11011$

Answer: a) 11000 b) 01101 c) 11001 d) 11011