Simplify $(x'+y)'(x+y)'$ with boolean algebra

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So I'm doing some homework and trying to simplify $(x'+y)'(x+y)'$. So far these are the steps I've completed, but I'm not 100% sure that they're appropriate.

$(x'+y)'(x+y)' = (x'+y)'(x’y’)$

$(x'+y)'(x’y’) = (x’’+ y’)(x’y’)$

$(x’’+y’)(x’y’) = (x+y’)(x’y’)$

I'm unsure of what to do after this step (or if I've made any actual mistakes)

edited Dec 2 at 7:23

Tianlalu

2,9451936

asked Oct 29 '14 at 2:18

Tai M.

2921218

add a comment |

up vote
0
down vote

favorite

So I'm doing some homework and trying to simplify $(x'+y)'(x+y)'$. So far these are the steps I've completed, but I'm not 100% sure that they're appropriate.

$(x'+y)'(x+y)' = (x'+y)'(x’y’)$

$(x'+y)'(x’y’) = (x’’+ y’)(x’y’)$

$(x’’+y’)(x’y’) = (x+y’)(x’y’)$

I'm unsure of what to do after this step (or if I've made any actual mistakes)

edited Dec 2 at 7:23

Tianlalu

2,9451936

asked Oct 29 '14 at 2:18

Tai M.

2921218

add a comment |

up vote
0
down vote

favorite

So I'm doing some homework and trying to simplify $(x'+y)'(x+y)'$. So far these are the steps I've completed, but I'm not 100% sure that they're appropriate.

$(x'+y)'(x+y)' = (x'+y)'(x’y’)$

$(x'+y)'(x’y’) = (x’’+ y’)(x’y’)$

$(x’’+y’)(x’y’) = (x+y’)(x’y’)$

I'm unsure of what to do after this step (or if I've made any actual mistakes)

edited Dec 2 at 7:23

Tianlalu

2,9451936

asked Oct 29 '14 at 2:18

Tai M.

2921218

So I'm doing some homework and trying to simplify $(x'+y)'(x+y)'$. So far these are the steps I've completed, but I'm not 100% sure that they're appropriate.

$(x'+y)'(x+y)' = (x'+y)'(x’y’)$

$(x'+y)'(x’y’) = (x’’+ y’)(x’y’)$

$(x’’+y’)(x’y’) = (x+y’)(x’y’)$

I'm unsure of what to do after this step (or if I've made any actual mistakes)

boolean-algebra

edited Dec 2 at 7:23

Tianlalu

2,9451936

asked Oct 29 '14 at 2:18

Tai M.

2921218

edited Dec 2 at 7:23

Tianlalu

2,9451936

asked Oct 29 '14 at 2:18

Tai M.

2921218

edited Dec 2 at 7:23

Tianlalu

2,9451936

edited Dec 2 at 7:23

Tianlalu

2,9451936

edited Dec 2 at 7:23

Tianlalu

2,9451936

asked Oct 29 '14 at 2:18

Tai M.

2921218

asked Oct 29 '14 at 2:18

Tai M.

2921218

asked Oct 29 '14 at 2:18

Tai M.

2921218

add a comment |

1 Answer
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up vote
0
down vote

$(x'+y)'(x+y)'=(x'+y)'(x'y')=(x''y')(x'y')=(xy')(x'y')$

Can you do the last step?

answered Oct 29 '14 at 2:32

Joel Reyes Noche

5,59733148

I couldn't figure it out algebraically so I drew out a truth table to figure it out and realized it was 0.
– Tai M.
Oct 29 '14 at 3:04

add a comment |

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1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

up vote
0
down vote

$(x'+y)'(x+y)'=(x'+y)'(x'y')=(x''y')(x'y')=(xy')(x'y')$

Can you do the last step?

answered Oct 29 '14 at 2:32

Joel Reyes Noche

5,59733148

I couldn't figure it out algebraically so I drew out a truth table to figure it out and realized it was 0.
– Tai M.
Oct 29 '14 at 3:04

add a comment |

up vote
0
down vote

$(x'+y)'(x+y)'=(x'+y)'(x'y')=(x''y')(x'y')=(xy')(x'y')$

Can you do the last step?

answered Oct 29 '14 at 2:32

Joel Reyes Noche

5,59733148

I couldn't figure it out algebraically so I drew out a truth table to figure it out and realized it was 0.
– Tai M.
Oct 29 '14 at 3:04

add a comment |

up vote
0
down vote

$(x'+y)'(x+y)'=(x'+y)'(x'y')=(x''y')(x'y')=(xy')(x'y')$

Can you do the last step?

answered Oct 29 '14 at 2:32

Joel Reyes Noche

5,59733148

$(x'+y)'(x+y)'=(x'+y)'(x'y')=(x''y')(x'y')=(xy')(x'y')$

Can you do the last step?

answered Oct 29 '14 at 2:32

Joel Reyes Noche

5,59733148

answered Oct 29 '14 at 2:32

Joel Reyes Noche

5,59733148

answered Oct 29 '14 at 2:32

Joel Reyes Noche

5,59733148

answered Oct 29 '14 at 2:32

Joel Reyes Noche

5,59733148

I couldn't figure it out algebraically so I drew out a truth table to figure it out and realized it was 0.
– Tai M.
Oct 29 '14 at 3:04

add a comment |

I couldn't figure it out algebraically so I drew out a truth table to figure it out and realized it was 0.
– Tai M.
Oct 29 '14 at 3:04

I couldn't figure it out algebraically so I drew out a truth table to figure it out and realized it was 0.
– Tai M.
Oct 29 '14 at 3:04

add a comment |

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