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Byju's Answer
Standard XII
Mathematics
Contra-Positive
Let Δ∈∧, ∨, ⇒...
Question
Let
Δ
∈
{
∧
,
∨
,
⇒
,
⇔
}
be such that
(
p
∧
q
)
Δ
(
(
p
∨
q
)
⇒
q
)
is a tautology. Then
Δ
is equal to :
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Solution
(
p
∨
q
)
⇒
q
∼
(
p
∨
q
)
∨
q
=
(
∼
p
∧
∼
q
)
∨
q
=
(
∼
p
∨
q
)
∧
(
∼
q
∨
q
)
=
(
∼
p
∨
q
)
∧
T
=
∼
p
∨
q
Now
(
p
∧
q
)
Δ
(
∼
p
∨
q
)
p
q
∼
p
p
∧
q
∼
p
∨
q
(
p
∧
q
)
Δ
(
∼
p
∨
q
)
T
T
F
T
T
T
T
F
F
F
F
T
F
T
T
F
T
T
F
F
T
F
T
T
∴
Δ
=
⇒
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11
Similar questions
Q.
Let
Δ
,
∇
∈
{
∧
,
∨
}
be such that
p
∇
q
⇒
(
(
p
Δ
q
)
∇
r
)
is a tautology. Then
(
p
∇
q
)
Δ
r
is logically equivalent to:
Q.
The number of choices for
Δ
∈
{
∧
,
∨
,
⇒
,
⇔
}
, such that
(
p
Δ
q
)
⇒
(
(
p
Δ
∼
q
)
∨
(
(
∼
p
)
Δ
q
)
)
is a tautology, is
Q.
Let
r
∈
{
p
,
q
,
∼
p
,
∼
q
}
be such that the logical statement
r
∨
(
∼
p
)
⇒
(
p
∧
q
)
∨
r
is a tautology. Then
r
is equal to :
Q.
Let
∗
,
□
∈
{
∧
,
∨
}
be such that Boolean expression
(
p
∗
∼
q
)
⇒
(
p
□
q
)
is a tautology. Then:
Q.
Let the operations
∗
,
⊙
∈
{
∧
,
∨
}
. If
(
p
∗
q
)
⊙
(
p
⊙
∼
q
)
is a tautology, then the ordered pair
(
∗
,
⊙
)
is
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