Question

relations in families pair people with other people. relations in algebra pair numbers with other numbers. here are some relations which involve numbers:
the \greater than\ relation: we will use g(x) to mean \a number greater than x.\
g(5)=7 means \a number greater than 5 is 7.\ or 7 > 5
g(5)=10.4 means \a number greater than 5 is 10.4.\ or 10.4 > 5
name some other numbers which can be paired up with 5 in this relation:
g(5)=
g(5)=
g(5)=
g(5)=
find a number to make each of these true:
g(2)=
g(-6)=
g(100)=
g(4.8)=
the \less than\ relation: we will use l(x) to mean \a number less than x.\
l(3)=2 means \a number less than 3 is 2.\ or 2 < 3
l(3)=-1\frac{1}{3} means \a number less than 3 is -1\frac{1}{3}.\ or -1\frac{1}{3}<3
l(-1)= means
l(-2.5)= means
the \equality\ relation: we will use e(x) to mean \a number equal to x.\
e(2)=2 means \a number equal to 2 is 2.\ or 2 = 2
e(-6)= means
e(11.2)= means
the \less than or equal to\ relation: we will use t(x) to mean \a number less than or equal to x.\
t(4)=0 means \a number less than or equal to 4 is 0.\ or 0 ≤ 4
t(\frac{3}{5})=\frac{3}{5} means
t(-6.3)= means

Explanation:

Step1: Understand the \(G(x)\) relation

The function \(G(x)\) represents a number greater than \(x\). So for each \(x\) value, we just need to pick a number larger than it.

Step2: Understand the \(L(x)\) relation

The function \(L(x)\) represents a number less than \(x\). So for each \(x\) value, we pick a number smaller than it.

Step3: Understand the \(E(x)\) relation

The function \(E(x)\) represents a number equal to \(x\), so the output is the same as the input.

Step4: Understand the \(T(x)\) relation

The function \(T(x)\) represents a number less than or equal to \(x\). For \(x=-6.3\), we can choose - 6.3 itself as it satisfies the less - than or equal condition.

Answer:

1. For \(G(5)\): Possible answers could be \(G(5)=8\), \(G(5)=12\), \(G(5)=5.5\), \(G(5)=9\)

• \(G(2)\): A number greater than 2, so \(G(2)=3\)
• \(G(- 6)\): A number greater than - 6, so \(G(-6)=0\)
• \(G(100)\): A number greater than 100, so \(G(100)=101\)
• \(G(4.8)\): A number greater than 4.8, so \(G(4.8)=5\)

1. For \(L(-1)\): A number less than - 1, so \(L(-1)=-2\), means "A number less than - 1 is - 2." or \(-2 < - 1\)

• \(L(-2.5)\): A number less than - 2.5, so \(L(-2.5)=-3\), means "A number less than - 2.5 is - 3." or \(-3 < - 2.5\)

1. For \(E(-6)\): A number equal to - 6, so \(E(-6)=-6\), means "A number equal to - 6 is - 6." or \(-6=-6\)

• \(E(11.2)\): A number equal to 11.2, so \(E(11.2)=11.2\), means "A number equal to 11.2 is 11.2." or \(11.2 = 11.2\)

1. For \(T(-6.3)\): A number less than or equal to - 6.3, so \(T(-6.3)=-6.3\), means "A number less than or equal to - 6.3 is - 6.3." or \(-6.3\leq - 6.3\)