Question

a = - 2/3 b = 1/5 c = 2/7 Verify a x (b – c) = (a x b) – (a x c).

Answer 1

GIVEN :-

• a = -2/3
• b = 1/5
• c = 2/7

TO VERIFY :-

• a × (b - c) = (a × b) - (a × c)

VERIFICATION :-

⇒ a × (b - c) = (a × b) - (a × c)

Put the value of a , b and c.

L.H.S = a × (b - c)

⇒ -2/3 × (1/5 - 2/7)

⇒ -2/3 × [(7 - 10)/35]

⇒ -2/3 × [ -3/35 ]

⇒ -2/3 × -3/35

⇒ 6/105 -----------------------(1)

R.H.S = (a × b) - (a × c)

⇒ (-2/3 × 1/5) - (-2/3 × 2/7)

⇒ (-2/15) - (-4/21)

⇒ -2/5 + 4/21

⇒ -14/105 + 20/105

⇒ (-14 + 20)/105

⇒ 6/105 ------------------------(2)

From Equation (1) and (2)

L.H.S = R.H.S

HENCE VERIFIED ✔

Answer 2

Answer:

Step-by-step explanation:

A ×B=${1, 3, 5} × {2,3} = [{1, 2},{1, 3},{3, 2},{3, 3},{5, 2},{5, 3}]$

B × A = ${2, 3} × {1, 3, 5} = [{2, 1},{2, 3},{2, 5},{3, 1},{3, 3},{3, 5}]$

A × A = ${1, 3, 5} × {1, 3, 5}= [{1, 1},{1, 3},{1, 5},{3, 1},{3, 3},{3, 5},{5, 1},{5, 3},{5, 5}]$

B × B =${2, 3} × {2, 3} = [{2, 2},{2, 3},{3, 2},{3, 3}]$

Note:

If either A or B are null sets, then A ×B will also be an empty set, i.e., if A = ∅ or

B = ∅, then A × B = ∅

hope it helps

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