Answer:
16
Step-by-step explanation:
father's age=46
half of father's age=46/2=23
Xiao's age=15
so when Xiao is half of her father age =23-15=8
then add 8 to his sister's age
so 8+8=16
hope its was helpful<3<3
plz rate the answer
i)On z, define a∗b=a−b
here aϵz
+
and bϵz
+
i.e.,a and b are positive integers
Let a=2,b=5⇒2∗5=2−5=−3
But −3 is not a positive integer
i.e., −3∈
/
z
+
hence,∗ is not a binary operation.
ii)On Q,define a∗b=ab−1
Check commutative
∗ is commutative if,a∗b=b∗a
a∗b=ab+1;a∗b=ab+1=ab+1
Since a∗b=b∗aforalla,bϵQ
∗ is commutative.
Check associative
∗ is associative if (a∗b)∗c=a∗(b∗c)
(a∗b)∗c=(ab+1)∗c=(ab+1)c+1=abc+c+1
a∗(b∗c)=a∗(bc+1)=a(bc+1)+1=abc+a+1
Since (a∗b)∗c
=a∗(b∗c)
∗ is not an associative binary operation.
iii)On Q,define a∗b=
2
ab
Check commutative
∗ is commutative is a∗b=b∗a
a∗b=
2
ab
b∗a=
2
ba
=
2
ab
a∗b=b∗a∀a,bϵQ
∗ is commutativve.
Check associative
∗ is associative if (a∗b)∗c=a∗(b∗c)
(a∗b)∗c=
2
(
2
ab
)∗c
=
4
abc
(a∗b)∗c=a∗(b∗c)=
2
a×
2
bc
=
4
abc
Since (a∗b)∗c=a∗(b∗c)∀a,b,cϵQ
∗ is an associative binary operation.
iv)On z
+
, define if a∗b=b∗a
a∗b=2
ab
b∗a=2
ba
=2
ab
Since a∗b=b∗a∀a,b,cϵz
+
∗ is commutative.
Check associative.
∗ is associative if $$
(a∗b)∗c=a∗(b∗c)
(a∗b)∗c=(2
ab
)
∗
c=2
2
ab
c
a∗(b∗c)=a∗(2
ab
)=2
a2
bc
Since (a∗b)∗c
=a∗(b∗c)
∗ is not an associative binary operation.
v)On z
+
define a∗b=a
b
a∗b=a
b
,b∗a=b
a
⇒a∗b
=b∗a
∗ is not commutative.
Check associative
∗ is associative if $$
(a∗b)∗c=a∗(b∗c)
(a∗b)∗c=(a
b
)
∗
c=(a
b
)
c
a∗(b∗c)=a∗(2
bc
)=2
a2
bc
eg:−Leta=2,b=3 and c=4
(a∗b)
∗
c=(2∗3)
∗
4=(2
3
)
∗
4=8∗4=8
4
a∗(b∗c)=2
∗
(3∗4)=2
∗
(3
4
)=2∗81=2
81
Since (a∗b)∗c
=a∗(b∗c)
∗ is not an associative binary operation.
vi)On R−{−1}, define a∗b=
b+1
a
Check commutative
∗ is commutative if a∗b=b∗a
a∗b=
b+1
a
b∗a=
a+1
b
Since a∗b
=b∗a
∗ is not commutatie.
Check associative
∗ is associative if (a∗b)∗c=a∗(b∗c)
(a∗b)∗c=(
b+1
a
)
∗
c=
c
b
a
+1
=
c(b+1)
a
a∗(b∗c)=a∗(
c+1
b
)=
c+1
b
a
=
b
a(c+1)
Since (a∗b)∗c
=a∗(b∗c)
∗ is not a associative binary operation
The given statement is An integer is divisible by 100 if and only if its last two digits are zeros.
The two conditional statements that can be made are:
1) If an integer is divisible by 100 its last two digits are zeros.
This is a true statement. If a number is divisible by 100, it means 100 must be a factor of that number. When 100 will be multiplied by the remaining factors, the number will have the last two digits zeros.
<h3>What happen when last two digit of the number are 0?</h3>
2) If the last two digits of an integer are zeros, it is divisible by 100.
This is also true. If the last two digits are zeros, this means 100 is a factor of the integer. So the number will be divisible by 100.
Therefore, the two conditional statements that are formed are both true.
So, option A is the correct answer.
Yes, it is. When the definition is separated into two conditional statements, both of the statements are true.
To learn more about the integer visit:
brainly.com/question/17695139
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