Question

using Venn diagram prove that for the sets x,yand z.
(x-y) - z = x - (y intersection z)​

Answer 1

Answer:

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Step-by-step explanation:

ANSWER

Let Δ=ω

∣

∣

∣

∣

∣

∣

∣

∣

x

x

2

y+z

y

y

2

x+z

z

z

2

x+y

∣

∣

∣

∣

∣

∣

∣

∣

Applying R

3

→R

3

+R

1

, we get

Δ=ω

∣

∣

∣

∣

∣

∣

∣

∣

x

x

2

x+y+z

y

y

2

x+y+z

z

z

2

x+y+z

∣

∣

∣

∣

∣

∣

∣

∣

=(x+y+z)ω

∣

∣

∣

∣

∣

∣

∣

∣

x

x

2

1

y

y

2

1

z

z

2

1

∣

∣

∣

∣

∣

∣

∣

∣

Applying C

1

→C

1

−C

2

and C

2

→C

2

−C

3

, we get

Δ=(x+y+z)ω

∣

∣

∣

∣

∣

∣

∣

∣

x−y

x

2

−y

2

0

y−z

y

2

−z

2

0

z

z

2

1

∣

∣

∣

∣

∣

∣

∣

∣

=(x+y+z)(x−y)(y−z)ω

∣

∣

∣

∣

∣

∣

∣

∣

1

x+y

0

1

y+z

0

z

z

2

1

∣

∣

∣

∣

∣

∣

∣

∣

Expanding along R

3

, we get

=(x+y+z)(x−y)(y−z)(y+z−x−y)

=(x−y)(y−z)(z−x)(x+y+z)